Subjects -> MATHEMATICS (Total: 1013 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (714 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (714 journals)            First | 1 2 3 4 | Last
 Showing 201 - 400 of 538 Journals sorted alphabetically Educação Matemática Debate Edumatica : Jurnal Pendidikan Matematika EduMatSains Electronic Journal of Differential Equations Electronic Journal of Graph Theory and Applications       (Followers: 3) Em Teia : Revista de Educação Matemática e Tecnológica Iberoamericana Emergent Scientist Energy for Sustainable Development       (Followers: 13) Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas Entropy       (Followers: 5) ESAIM: Control Optimisation and Calculus of Variations       (Followers: 2) Euclid European Journal of Applied Mathematics European Journal of Combinatorics       (Followers: 3) European Journal of Mathematics       (Followers: 1) European Scientific Journal       (Followers: 1) Examples and Counterexamples Experimental Mathematics       (Followers: 5) Expositiones Mathematicae       (Followers: 2) Extracta Mathematicae Facta Universitatis, Series : Mathematics and Informatics Finite Fields and Their Applications       (Followers: 5) Fixed Point Theory and Applications Formalized Mathematics Forum of Mathematics, Pi       (Followers: 1) Forum of Mathematics, Sigma       (Followers: 1) Foundations and Trends® in Econometrics       (Followers: 6) Foundations and Trends® in Networking       (Followers: 1) Foundations and Trends® in Stochastic Systems       (Followers: 1) Foundations and Trends® in Theoretical Computer Science       (Followers: 1) Foundations of Computational Mathematics Fractal and Fractional Fractals       (Followers: 1) Frontiers of Mathematics in China Fuel Cells Bulletin       (Followers: 9) Functional Analysis and Other Mathematics       (Followers: 4) Fundamental Journal of Mathematics and Applications Funktsional'nyi Analiz i ego Prilozheniya Fuzzy Optimization and Decision Making       (Followers: 8) Game Theory       (Followers: 2) Games       (Followers: 4) Games and Economic Behavior       (Followers: 26) Gamm - Mitteilungen GANIT : Journal of Bangladesh Mathematical Society GEM - International Journal on Geomathematics       (Followers: 1) General Mathematics Glasgow Mathematical Journal Global Journal of Mathematical Sciences Graphs and Combinatorics       (Followers: 4) Grey Systems : Theory and Application Groups, Complexity, Cryptology       (Followers: 2) GSTF Journal of Mathematics, Statistics and Operations Research       (Followers: 1) Historia Mathematica Historical Methods: A Journal of Quantitative and Interdisciplinary History       (Followers: 28) IMA Journal of Applied Mathematics IMA Journal of Numerical Analysis - advance access ImmunoInformatics       (Followers: 1) Indagationes Mathematicae Indian Journal of Pure and Applied Mathematics       (Followers: 4) Indonesian Journal of Combinatorics Indonesian Journal of Science and Mathematics Education       (Followers: 2) Infinite Dimensional Analysis, Quantum Probability and Related Topics       (Followers: 1) Infinity Jurnal Matematika dan Aplikasinya       (Followers: 4) Information and Inference InfoTekJar : Jurnal Nasional Informatika dan Teknologi Jaringan InfraMatics Insight - Non-Destructive Testing and Condition Monitoring       (Followers: 114) International Electronic Journal of Algebra International Journal for Numerical Methods in Engineering       (Followers: 37) International Journal for Numerical Methods in Fluids       (Followers: 20) International Journal of Advanced Mathematical Sciences International Journal of Advanced Mechatronic Systems       (Followers: 2) International Journal of Advanced Research in Mathematics International Journal of Advances in Engineering Sciences and Applied Mathematics       (Followers: 10) International Journal of Algebra and Computation       (Followers: 1) International Journal of Algebra and Statistics       (Followers: 3) International Journal of Applied and Computational Mathematics International Journal of Applied Mathematical Research       (Followers: 1) International Journal of Applied Mathematics and Computer Science       (Followers: 7) International Journal of Applied Mechanics       (Followers: 8) International Journal of Applied Nonlinear Science International Journal of Autonomic Computing       (Followers: 1) International Journal of Bifurcation and Chaos       (Followers: 4) International Journal of Biomathematics       (Followers: 2) International Journal of Computational Complexity and Intelligent Algorithms International Journal of Computational Economics and Econometrics       (Followers: 6) International Journal of Computational Geometry and Applications       (Followers: 2) International Journal of Computational Intelligence and Applications       (Followers: 2) International Journal of Computational Methods       (Followers: 4) International Journal of Computer Processing Of Languages       (Followers: 1) International Journal of Control, Automation and Systems       (Followers: 15) International Journal of Dynamical Systems and Differential Equations       (Followers: 1) International Journal of Economics and Accounting       (Followers: 1) International Journal of Foundations of Computer Science       (Followers: 3) International Journal of Fuzzy Computation and Modelling       (Followers: 2) International Journal of Image and Graphics       (Followers: 5) International Journal of Industrial Electronics and Drives       (Followers: 3) International Journal of Low-Carbon Technologies       (Followers: 1) International Journal of Mathematical Education in Science and Technology       (Followers: 9) International Journal of Mathematical Modelling & Computations       (Followers: 3) International Journal of Mathematical Modelling and Numerical Optimisation       (Followers: 5) International Journal of Mathematical Sciences and Computing International Journal of Mathematics       (Followers: 4) International Journal of Mathematics & Computation International Journal of Mathematics and Mathematical Sciences       (Followers: 4) International Journal of Mathematics in Operational Research       (Followers: 2) International Journal of Metaheuristics       (Followers: 1) International Journal of Modelling in Operations Management       (Followers: 2) International Journal of Modern Nonlinear Theory and Application       (Followers: 1) International Journal of Number Theory       (Followers: 2) International Journal of Partial Differential Equations       (Followers: 2) International Journal of Polymer Science       (Followers: 25) International Journal of Pure Mathematical Sciences International Journal of Reliability, Quality and Safety Engineering       (Followers: 14) International Journal of Research in Undergraduate Mathematics Education       (Followers: 5) International Journal of Sediment Research       (Followers: 2) International Journal of Shape Modeling       (Followers: 1) International Journal of Theoretical and Mathematical Physics       (Followers: 13) International Journal of Trends in Mathematics Education Research       (Followers: 5) International Journal of Ultra Wideband Communications and Systems International Journal of Wavelets, Multiresolution and Information Processing International Journal on Artificial Intelligence Tools       (Followers: 9) International Mathematics Research Notices       (Followers: 1) Internet Mathematics       (Followers: 1) Inventiones mathematicae       (Followers: 3) Inverse Problems in Science and Engineering       (Followers: 3) Investigations in Mathematics Learning Iranian Journal of Optimization       (Followers: 2) Israel Journal of Mathematics Ithaca : Viaggio nella Scienza ITM Web of Conferences Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Jahresbericht der Deutschen Mathematiker-Vereinigung Japan Journal of Industrial and Applied Mathematics Japanese Journal of Mathematics JIPM (Jurnal Ilmiah Pendidikan Matematika) JMPM : Jurnal Matematika dan Pendidikan Matematika JOHME : Journal of Holistic Mathematics Education       (Followers: 3) Johnson Matthey Technology Review Jornal Internacional de Estudos em Educação Matemática Journal d'Analyse Mathématique       (Followers: 2) Journal de Mathématiques Pures et Appliquées       (Followers: 3) Journal for Research in Mathematics Education       (Followers: 29) Journal für Mathematik-Didaktik Journal of Advanced Mathematics and Applications       (Followers: 1) Journal of Algebra       (Followers: 3) Journal of Algebra and Its Applications       (Followers: 3) Journal of Algebraic Combinatorics       (Followers: 3) Journal of Algorithms & Computational Technology Journal of Applied Mathematics       (Followers: 3) Journal of Applied Mathematics and Computation       (Followers: 2) Journal of Applied Mathematics and Computing Journal of Applied Mathematics, Statistics and Informatics       (Followers: 1) Journal of Artificial Intelligence and Data Mining       (Followers: 10) Journal of Classification       (Followers: 5) Journal of Combinatorial Designs       (Followers: 4) Journal of Combinatorial Optimization       (Followers: 7) Journal of Combinatorial Theory, Series A       (Followers: 5) Journal of Combinatorial Theory, Series B       (Followers: 3) Journal of Complex Analysis       (Followers: 2) Journal of Complex Networks       (Followers: 1) Journal of Complexity       (Followers: 6) Journal of Computational and Applied Mathematics       (Followers: 6) Journal of Computational Biology       (Followers: 9) Journal of Computational Mathematics and Data Science Journal of Computational Multiphase Flows       (Followers: 1) Journal of Computational Physics       (Followers: 60) Journal of Computational Physics : X       (Followers: 1) Journal of Computer Engineering, System and Science (CESS) Journal of Contemporary Mathematical Analysis Journal of Cryptology       (Followers: 5) Journal of Difference Equations and Applications Journal of Differential Equations       (Followers: 1) Journal of Discrete Mathematics       (Followers: 1) Journal of Dynamics and Differential Equations Journal of Engineering Mathematics       (Followers: 2) Journal of Evolution Equations Journal of Experimental Algorithmics Journal of Flood Risk Management       (Followers: 14) Journal of Function Spaces Journal of Functional Analysis       (Followers: 3) Journal of Geochemical Exploration       (Followers: 4) Journal of Geological Research       (Followers: 1) Journal of Geovisualization and Spatial Analysis Journal of Global Optimization       (Followers: 6) Journal of Global Research in Mathematical Archives Journal of Homotopy and Related Structures Journal of Honai Math Journal of Humanistic Mathematics       (Followers: 1) Journal of Hyperbolic Differential Equations Journal of Indian Council of Philosophical Research Journal of Industrial Mathematics       (Followers: 2) Journal of Inequalities and Applications Journal of Infrared, Millimeter and Terahertz Waves       (Followers: 3) Journal of Integrable Systems Journal of Knot Theory and Its Ramifications       (Followers: 2) Journal of Liquid Chromatography & Related Technologies       (Followers: 7) Journal of Logical and Algebraic Methods in Programming       (Followers: 1) Journal of Manufacturing Systems       (Followers: 3) Journal of Mathematical Analysis and Applications       (Followers: 3)

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Similar Journals
 Journal d'Analyse MathématiqueJournal Prestige (SJR): 1.262 Citation Impact (citeScore): 1Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0021-7670 - ISSN (Online) 1565-8538 Published by Springer-Verlag  [2469 journals]
• Spectral structure of the Neumann–Poincaré operator on thin
domains in two dimensions

Abstract: Abstract We consider the spectral structure of the Neumann–Poincaré operators defined on the boundaries of thin domains of rectangular shape in two dimensions. We prove that as the aspect ratio of the domains tends to ∞, or equivalently, as the domains get thinner, the spectra of the Neumann–Poincaré operators are densely distributed in [−1/2, 1/2], the interval which contains the spectrum of Neumann–Poincaré operators.
PubDate: 2022-06-03

• Möbius orthogonality of sequences with maximal entropy

Abstract: Abstract We prove that strongly b-multiplicative functions of modulus 1 along squares are asymptotically orthogonal to the Möbius function. This provides examples of sequences having maximal entropy and satisfying this property.
PubDate: 2022-06-03

• Formation of singularities for multi-dimensional transport equations with
nonlocal velocity

Abstract: Abstract This paper is concerned with a class of multi-dimensional transport equations with nonlocal velocity. It is shown that the local smooth solution cannot exist globally in time via the De Giorgi iteration technique.
PubDate: 2022-06-03

• Comparison radius and mean topological dimension: Rokhlin property,
comparison of open sets, and subhomogeneous C-algebras

Abstract: Abstract Let (X, Γ) be a free minimal dynamical system, where X is a compact separable Hausdorff space and Γ is a discrete amenable group. It is shown that, if (X, Γ) has a version of Rokhlin property (uniform Rokhlin property) and if C(X) ⋊ Γ has a Cuntz comparison on open sets, then the comparison radius of the crossed product C*-algebra C(X) ⋊ Γ is at most half of the mean topological dimension of (X, Γ). These two conditions are shown to be satisfied if Γ = ℤ or if (X, Γ) is an extension of a free Cantor system and Γ has subexponential growth. The main tools being used are Cuntz comparison of diagonal elements of a subhomogeneous C*-algebra and small subgroupoids.
PubDate: 2022-06-03

• On the dimension of the k-medial axis for an arbitrary closed set

Abstract: Abstract We prove that the k-medial axis of an arbitrary closed set in ℝn is (n − k + 1)-rectifiable (and hence of dimension at most n − k +1). This result gives a first stratification for the medial axis of any closed set, which has been widely studied and used in pure and applied mathematics. This also answers a question proposed by Erdös [4], and leads to more further interesting investigations (see the end of the article).
PubDate: 2022-06-03

• A T1 theorem for general Calderón—Zygmund operators with comparable
doubling weights, and optimal cancellation conditions

Abstract: Abstract We begin an investigation into extending the T1 theorem of David and Journé, and the corresponding optimal cancellation conditions of Stein, to more general pairs of distinct doubling weights. For example, when 0 < α < n, and σ and ω are A∞ weights satisfying the one-tailed Muckenhoupt conditions, and Kα is a smooth fractional CZ kernel, we show there exists a bounded operator Tα: L2(σ) → L2(ω) associated with Kα if and only if there is a positive constant $${\mathfrak{A}_{{K^\alpha }}}(\sigma ,\omega )$$ so that $$\matrix{ \hfill {\int_{\left\ {x - {x_0}} \right\ < N} {{{\left {\int_{\varepsilon < \left\ {x - y} \right\ < N} {{K^\alpha }(x,y)d\sigma (y)} } \right }^2}d\omega (x) \le {\mathfrak{A}_{{K^\alpha }}}(\sigma ,\omega )\int_{\left\ {{x_0} - y} \right\ < N} {d\sigma (y),} } } \cr \hfill {{\rm{for}}\,{\rm{all}}\,0 < \varepsilon < N\,{\rm{and}}\,{x_0} \in {\mathbb{R}^n},} \cr }$$ where ‖y‖ ≡ max1≤k≤n ∣yk∣, along with a dual inequality. More generally this holds for measures σ and ω comparable in the sense of Coifman and Fefferman that satisfy a fractional Ask{∞/α} condition. These results are deduced from the following theorem of T1 type, namely that if σ and ω are doubling measures, comparable in the sense of Coifman and Fefferman, and satisfying one-tailed Muckenhoupt conditions, then Tα: L2(σ) → L2(ω) if and only if the dual pair of testing conditions hold, as well as a strong form of the weak boundedness property, $$\left {\int_F {\left( {{T^\alpha }{{\bf{1}}_E}} \right)d\omega } } \right \le {\cal B}{\cal J}{\cal C}{{\cal T}_{{T^\alpha }}}(\sigma ,\omega )\sqrt {{{\left {{Q_\sigma }} \right }_\sigma }{{\left {{Q_\sigma }} \right }_{\omega ,}}} \,\,\,\,{\rm{for}}\,{\rm{all}}\,{\rm{cubes}}\,Q \subset {\mathbb{R}^n},$$ where $${\cal B}{\cal J}{\cal C}{{\cal T}_{{T^\alpha }}}(\sigma ,\omega )$$ is a positive constant called the bilinear cube/indicator testing constant. The comparability of measures and the bilinear cube/indicator testing condition can both be dropped if the stronger indicator/cube testing conditions are assumed.
PubDate: 2022-06-03

• On a Theorem of Wolff Revisited

Abstract: Abstract We study p-harmonic functions, 1 < p ≠ 2 < ∞, in ℝ + 2 = {z = x + iy: y > 0, −∞ < x < ∞} and B(0, 1) = {z: ∣z∣ < 1}. We first show for fixed p,1 < p ≠ 2 < ∞, and for all large integers N ≥ N0 that there exists a p-harmonic function on B(0, 1), V = V(reiθ), which is 2π/N periodic in the θ variable, and Lipschitz continuous on ∂B(0, 1) with Lipschitz norm ≤ cN, satisfying V(0) = 0 and $${c^{ - 1}} \le \int_{ - \pi }^\pi {V({e^{i\theta }})d\theta \le c}$$ . In case 2 < p < ∞ we give a more or less explicit example of V and our work is an extension of a result of Wolff in [Wol07, Lemma 1] on ℝ + 2 to B(0, 1). Using our first result, we extend the work of Wolff in [Wol07] on the failure of Fatou type theorems for ℝ + 2 to B(0, 1) for p-harmonic functions, 1 < p ≠ 2 < ∞. Finally, we also outline the modifications needed for extending the work of Llorente, Manfredi, and Wu in [LMW05] regarding the failure of subadditivity of p-harmonic measure on ∂ℝ + 2 to ∂B(0, 1).
PubDate: 2022-06-03

• Liouville-type results for spherical symmetric linear differential
operators with constant coefficients

Abstract: Abstract Let P(z) be a polynomial. We study the equation P(Δ)u = 0 as well as the inequalities P(Δ)u ≥ 0, and P(Δ)u ≥ f (u) on the whole ℝn. We prove some Liouville-type results for nonnegative solutions and for solutions having a natural growth condition at infinity.
PubDate: 2022-06-03

• On the packing dimension of Furstenberg sets

Abstract: Abstract We prove that if α ∈ (0, 1/2], then the packing dimension of a set E ⊂ ℝ2 for which there exists a set of lines of dimension 1 intersecting E in Hausdorff dimension ≥ α is at least 1/2 + α + c(α)for some c(α) > 0. In particular, this holds for α-Furstenberg sets, that is, sets having intersection of Hausdorff dimension ≥ ≥ with at least one line in every direction. Together with an earlier result of T. Orponen, this provides an improvement for the packing dimension of α-Furstenberg sets over the “trivial” estimate for all values of α ∈ (0, 1). The proof extends to more general families of lines, and shows that the scales at which an α-Furstenberg set resembles a set of dimension close to 1/2 + α, if they exist, are rather sparse.
PubDate: 2022-06-03

• Le poids des polynômes irréductibles à coefficients dans un
corps fini

Abstract: Résumé Ce travail concerne le poids des polynômes irréductibles sur un corps fini, c’est à dire le nombre de coefficients non nuls de ces polynômes. Nous introduisons un analogue polynomial de la méthode de Vinogradov développée par Gallagher et Vaughan afin de majorer les sommes d’exponentielles associées. Cela nous permet d’une part d’étudier la répartition dans les progressions arithmétiques du poids des polynômes irréductibles et d’autre part de donner une estimation asymptotique (avec terme d’erreur) du nombre de polynômes irréductibles de degré fixé ayant un poids donné proche de la valeur moyenne.
PubDate: 2022-06-03

• Correction to “Local asymptotics for orthonormal polynomials on the unit
circle via universality”

PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0196-x

• Non-boundedness of the number of super level domains of eigenfunctions

Abstract: Abstract Generalizing Courant’s nodal domain theorem, the “Extended Courant property” is the statement that a linear combination of the first n eigenfunctions has at most n nodal domains. A related question is to estimate the number of connected components of the (super) level sets of a Neumann eigenfunction u. Indeed, in this case, the first eigenfunction is constant, and looking at the level sets of u amounts to looking at the nodal sets {u − a = 0}, where a is a real constant. In the first part of the paper, we prove that the Extended Courant property is false for the subequilateral triangle and for regular N-gons (N large), with the Neumann boundary condition. More precisely, we prove that there exists a Neumann eigenfunction uk of the N-gon, with labeling k, 4 ≤ k ≤ 6, such that the set {uk ≠ 1} has (N + 1) connected components. In the second part, we prove that there exists a metric g on $$\mathbb{T}^{2}$$ (resp. on $$\mathbb{S}^{2}$$ ), which can be chosen arbitrarily close to the flat metric (resp. round metric), and an eigenfunction u of the associated Laplace—Beltrami operator, such that the set {u ≠ 1} has infinitely many connected components. In particular, the Extended Courant property is false for these closed surfaces. These results are strongly motivated by a recent paper by Buhovsky, Logunov and Sodin. As for the positive direction, in Appendix B, we prove that the Extended Courant property is true for the isotropic quantum harmonic oscillator in ℝ2.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0189-9

• Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

Abstract: Abstract In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov—Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We prove a two-term asymptotic formula for sloshing eigenvalues. In particular, this confirms a conjecture posed by Fox and Kuttler in 1983. We also obtain similar eigenvalue asymptotics for other related mixed Steklov type problems, and discuss applications to the study of Steklov spectral asymptotics on polygons.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0188-x

• Oscillatory Loomis—Whitney and Projections of Sublevel Sets

Abstract: Abstract We consider an oscillatory integral operator with Loomis—Whitney multilinear form. The phase is real analytic in a neighborhood of the origin in ℝd and satisfies a nondegeneracy condition related to its Newton polyhedron. Maximal decay is obtained for this operator in certain cases, depending on the Newton polyhedron of the phase and the given Lebesgue exponents. Our estimates imply volumes of sublevel sets of such real analytic functions are small relative to the product of areas of projections onto coordinate hyperplanes.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0190-3

• Seminorms for multiple averages along polynomials and applications to
joint ergodicity

Abstract: Abstract Exploiting the recent work of Tao and Ziegler on the concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria of joint ergodicity for sequences of the form $$(T_{1}^{p_{1,j}(n)}\cdots T_{d}^{p_{d,j}(n)})_{n\in\mathbb{Z}}$$ , 1 ≤ j ≤ k, where T1, …, Td are commuting measure preserving transformations on a probability measure space and pi, j are integer polynomials. To be more precise, we provide a sufficient condition for such sequences to be jointly ergodic, giving also a characterization for sequences of the form $$(T_{i}^{p(n)})_{n\in\mathbb{Z}}$$ , 1 ≤ i ≤ d to be jointly ergodic, answering a question due to Bergelson.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0186-z

• Generalized eigenfunctions and eigenvalues: A unifying framework for
Shnol-type theorems

Abstract: Abstract Let H be a generalized Schrödinger operator on a domain of a non-compact connected Riemannian manifold, and a generalized eigenfunction u for H: that is, u satisfies the equation Hu = λu in the weak sense but is not necessarily in L2. The problem is to find conditions on the growth of u, so that λ belongs to the spectrum of H. We unify and generalize known results on this problem. In addition, a variety of examples is provided, illustrating the different nature of the growth conditions.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0191-2

• Obstructions for automorphic quasiregular maps and Lattès-type
uniformly quasiregular maps

Abstract: Abstract Suppose that M is a closed, connected, and oriented Riemannian n-manifold, f: ℝn → M is a quasiregular map automorphic under a discrete group Γ of Euclidean isometries, and f has finite multiplicity in a fundamental cell of Γ. We show that if Γ has a sufficiently large translation subgroup ΓT, then dim Γ ∈ {0, n − 1, n}. If f is strongly automorphic and induces a non-injective Lattès-type uniformly quasiregular map, then the same assertion holds without the assumption on the size of ΓT. Moreover, an even stronger restriction holds in the Lattès case if M is not a rational cohomology sphere.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0187-y

• Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases

Abstract: Abstract We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart [22] and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The proofs combine energy estimates and variational methods.
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0170-7

• Singular integrals on C1,α regular curves in Carnot groups

Abstract: Abstract Let $$\mathbb{G}$$ be any Carnot group. We prove that if a convolution type singular integral associated with a 1-dimensional Calderón—Zygmund kernel is L2-bounded on horizontal lines, with uniform bounds, then it is bounded in Lp, p ∈ (1, ∞), on any compact C1, α, α ∈ (0, 1], regular curve in $$\mathbb{G}$$ .
PubDate: 2021-12-31
DOI: 10.1007/s11854-021-0194-z

• Spherical means on the Heisenberg group: Stability of a maximal function
estimate

Abstract: Abstract Consider the surface measure μ on a sphere in a nonvertical hyperplane on the Heisenberg group ℍn, n ≥ 2, and the convolution f * μ. Form the associated maximal function Mf = supt>0 ∣f * μt∣ generated by the automorphic dilations. We use decoupling inequalities due to Wolff and Bourgain—Demeter to prove Lp-boundedness of M in an optimal range.
PubDate: 2021-12-14
DOI: 10.1007/s11854-021-0171-6

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