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Similar Journals
 Journal of Pseudo-Differential Operators and ApplicationsJournal Prestige (SJR): 0.664 Citation Impact (citeScore): 1Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1662-9981 - ISSN (Online) 1662-999X Published by Springer-Verlag  [2658 journals]
• Nonnegative solutions and multiple solutions for a class of weighted
Hamiltonian subelliptic systems

Abstract: Abstract In this paper, we investigate existence results for the following system \begin{aligned} \left\{ \begin{aligned}&-\Delta _X u= v ^{p-1}v{\omega _1(x)}, \\&-\Delta _X v= u ^{q-1}u{\omega _2(x)}, x\in \Omega \subset {\mathbb {R}}^N \end{aligned} \right. \end{aligned} with homogeneous Dirichlet boundary conditions, where $$X=\{X_{1},X_{2},\ldots ,X_{m}\}$$ is a system of smooth vector fields defined on a neighborhood of $${\overline{\Omega }}$$ that satisfies the Hörmander’s condition, $$\triangle _{X}= -\sum _{i=1}^{m}X_{i}^{*} X_i$$ on $$\Omega$$ . Furthermore, $$\partial \Omega$$ is non-characteristic with respect to X and the weights $$\omega _i(x)$$ satisfy certain growth conditions involving negative powers of the C–C metric to isolated singular points. We construct a proper functional setting and use a version of linking theorem to examine the existence of nontrivial solutions where the growth of nonlinearities (p, q) are below certain critical hyperbola related to the generalized Métivier index of X. This work extends the results in Djairo G. de Figueiredo et al. (Annali di Matematica 187:531–545, 2008) to the class of subelliptic finitely degenerate operators and improves the recent multiple solutions in C.T. Anh et al. (Adv Nonlinear Anal 8(1): 661–678, 2017) to the case of superlinear system. Furthermore, the existence of nonnegative solutions and ground-state solutions is proved.
PubDate: 2021-10-07

• $$L^p$$ L p properties of non-Archimedean fractional differentiation
operators

Abstract: Abstract Let $$D^{\alpha }$$ be the Vladimirov–Taibleson fractional differentiation operator acting on complex-valued functions on a non-Archimedean local field. The identity $$D^{\alpha }D^{-\alpha }f=f$$ was known only for the case where f has a compact support. Following a result by Samko about the fractional Laplacian of real analysis, we extend the above identity in terms of $$L^p$$ -convergence of truncated integrals. Differences between real and non-Archimedean cases are discussed.
PubDate: 2021-10-05

• Different approach to the decomposition theory of $$HM^p_{q,{\varDelta _{\nu }}}$$ H M q , Δ ν p Hardy–Morrey spaces

Abstract: Abstract B-maximal functions in $$HM^p_{q,{\varDelta _{\nu }}}$$ Hardy–Morrey spaces, related to a Laplace–Bessel differential operator, are studied. We give B-maximal characterization of $$HM^p_{q,{\varDelta _{\nu }}}$$ Hardy–Morrey spaces and study the atomic decomposition theory which has the same cancellation properties of the $$H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})$$ Hardy spaces.
PubDate: 2021-10-04

• Amrein–Berthier and Logvinenko–Sereda uncertainty principles for the
Hankel–Stockwell transform

Abstract: Abstract The aim of this paper is to prove two new uncertainty principles for the Hankel–Stockwell transform namely Amrein–Berthier and Logvinenko–Sereda theorems.
PubDate: 2021-10-04

• Equivalence of K-functionals and modulus of smoothness for Laguerre type
operator

Abstract: Abstract The aim of this article is to establish the equivalence between a K-functional and a modulus of smoothness generated by $$D{\alpha }$$ operator on $${\mathbb {K}}$$ in the metrics of $$L^{2}_{\alpha }({\mathbb {K}})$$ with a certain weight.
PubDate: 2021-09-27

• Two classes of bilinear fractional integral operators and their
commutators on generalized fractional Morrey spaces

Abstract: Abstract In this paper, the authors prove that the following form of bilinear fractional integral operator \begin{aligned} B_{\alpha }(f,g)(x):=\int _{\mathbb {R}^{n}}\frac{f(x-y)g(x+y)}{ y ^{n-\alpha }}\mathrm {d}y \end{aligned} is bounded from the product of generalized fractional Morrey spaces $${\mathcal {L}}^{p_{1},\eta _{1},\varphi }(\mathbb {R}^{n})\times {\mathcal {L}}^{p_{2},\eta _{2},\varphi }(\mathbb {R}^{n})$$ to space $${\mathcal {L}}^{q,\eta -\alpha ,\varphi }(\mathbb {R}^{n})$$ , and also bounded from the product space $${\mathcal {L}}^{p_{1},\varphi }$$ $$(\mathbb {R}^{n})\times {\mathcal {L}}^{p_{2},\varphi }(\mathbb {R}^{n})$$ to $${\mathcal {L}}^{q,\varphi ^{\frac{q}{p}}}(\mathbb {R}^{n})$$ . Moreover, the boundedness of commutator $$[b_{1},b_{2},{\mathcal {I}}_{\alpha }]$$ generated by $$b_{1}, b_{2}\in \mathrm {BMO}(\mathbb {R}^{n})$$ and bilinear fractional integral operator $${\mathcal {I}}_{\alpha }$$ defined as in (1.1) is bounded from the product space $${\mathcal {L}}^{p_{1},\eta _{1},\varphi }(\mathbb {R}^{n})\times {\mathcal {L}}^{p_{2},\eta _{2},\varphi }(\mathbb {R}^{n})$$ to space $${\mathcal {L}}^{q,\eta -\alpha ,\varphi }(\mathbb {R}^{n})$$ ; as a corollary, the boundedness of the commutator $$[b_{1},b_{2},{\mathcal {I}}_{\alpha }]$$ on generalized Morrey space is also obtained.
PubDate: 2021-09-26

• Group classification and constructing conservation laws for

Abstract: Abstract Finding the symmetries and conservation laws of the nonlinear fractional differential equations are topics, which have many applications in various fields of science and engineering. In this manuscript, firstly, by using the Lie symmetry analysis, we obtain the Lie point symmetries of the time-fractional Sawada–Kotera–Parker–Dye equation. After that, by using the infinitesimal generators, we present the corresponding reduced fractional differential equations and fractional conservation laws.
PubDate: 2021-09-18

• Elliptic boundary value problems associated with isometric group actions

Abstract: Abstract Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators acting on functions on the manifold and its boundary. Provided that the group is of polynomial growth and its action is isometric, we construct a Chern character for elliptic elements in this algebra with values in a de Rham type cohomology of the fixed point manifolds for the group action and obtain an index formula in terms of this Chern character. Our index formula contains as special cases the index formula by Fedosov for boundary value problems in the Boutet de Monvel algebra and the index formula by Nazaikinskii, Savin and Sternin for operators on a closed manifold associated with an isometric group action.
PubDate: 2021-09-15

• The convergence constants and non linear approximations of fusion frames

Abstract: Abstract In this paper, we study the unconditional constant and nonlinear N-term approximation of fusion frames in Hilbert spaces. We show that the unconditional constant and greedy constant are bounded by a constant which is associated with the fusion frame bounds. We prove that the unconditional constant of cross fusion frame expansions satisfies the similar properties as long as the cross g-frame expansions stay uniformly bounded away from zero. Finally, we show that fusion frames satisfy the quasi greedy and almost greedy conditions. Moreover, we prove that fusion Riesz bases satisfy the greedy condition.
PubDate: 2021-08-29

• Nonlinear commutators on Morrey–Banach spaces

Abstract: Abstract We establish the boundedness of the nonlinear commutator introduced by Rochberg and Weiss (Ann Math 118:315–347, 1983) on Morrey–Banach spaces. In particular, we have the boundedness results on the Morrey–Lorentz spaces and the Morrey spaces with variable exponents.
PubDate: 2021-08-20

• Uncertainty principles for the offset linear canonical transform

Abstract: Abstract In this paper, we extend some different uncertainty principles (UPs), including Miyachi’s UP and Morgan’s UP for the offset linear canonical transform (OLCT) which provides a more general framework for a number of well-known linear integral transforms such as Fourier transform, fractional Fourier transform, linear canonical transform.
PubDate: 2021-08-16

• An interplay between parameter (p, q)-Boas transform and linear
canonical transform

Abstract: Abstract In this paper, we define and study parameter (p, q)-Boas transform of a signal in linear canonical transform domain. Also, we define the complex signals associated with parameter (p, q)-Boas transform and linear canonical transform and prove the generalized Boas transform product theorem (an analog of Bedrosian’s theorem) in the linear canonical transform domain. Further, using a linear combination of a signal and its parameter (p, q)-Boas transform, we define a $$\eta$$ -linear canonical Boas transform and study some of its properties. Finally, we propose some $$\eta$$ -linear canonical complex signals and give analysis of their linear canonical transform spectrum and eigenfunction property.
PubDate: 2021-08-10

• Gabor multipliers associated with the Bessel–Kingman hypergroup

Abstract: Abstract We consider the Bessel–Kingman hypergroup $$\big ([0,+\infty [,*\big )$$ and we denote by $$d\mu _\alpha ,\ \alpha \geqslant -\frac{1}{2},\$$ the measure defined on $$[0,+\infty [$$ by $$d\mu _\alpha (x)=\frac{x^{2+1}}{2^\alpha \ \Gamma (\alpha +1)}\ dx.\$$ We define the Gabor multiplier $$\mathscr {G}_{u,v}(\sigma )$$ associated with two square integrable functions u, v on $$[0,+\infty [$$ with respect to the measure $$d\mu _\alpha$$ called window functions and $$\sigma$$ is a measurable function on $$[0,+\infty [$$ called a signal. We prove that $$\mathscr {G}_{u,v}(\sigma )$$ is a bounded linear operator on $$L^2(d\mu _\alpha )$$ and it is compact. Next, we define the Schatten von-Neumann class $$S^p,\ p\in \ [1,+\infty ],\$$ and we show that the Gabor multiplier $$\mathscr {G}_{u,v}(\sigma )$$ belongs to the class $$S^p.\$$ We give also a formula of trace when $$\sigma \in \ L^1(d\mu _\alpha )$$ . Also, we define the Landau–Pollak–Slebian operator and we give its connection with the Gabor multiplier. Last, we study the boundedness and compactness of the Gabor multipliers for more window functions $$u,v\in \ L^p(d\mu _\alpha ),\ p\in \ [1,+\infty ]$$ .
PubDate: 2021-07-27

• Pseudo-fractional differential equations and generalized g-Laplace
transform

Abstract: Abstract In this article, we introduce a generalized g-Laplace transform and discuss some essential results of integral transform theory, in particular, involving a $$\psi$$ -Hilfer pseudo-fractional derivative and function convolution. In this sense, we investigated the existence and uniqueness of known solutions for a pseudo-fractional differential equation.
PubDate: 2021-07-24

• Semilinear wave equation on compact Lie groups

Abstract: Abstract In this note, we study the semilinear wave equation with power nonlinearity $$u ^p$$ on compact Lie groups. First, we prove a local in time existence result in the energy space via Fourier analysis on compact Lie groups. Then, we prove a blow-up result for the semilinear Cauchy problem for any $$p>1$$ , under suitable sign assumptions for the initial data. Furthermore, sharp lifespan estimates for local (in time) solutions are derived.
PubDate: 2021-07-14

• Fundamental solutions and decay rates for evolution problems on the torus
$$\mathbb {T}^n$$ T n

Abstract: Abstract In this paper we study large-time behavior evolution problems on the n-dimensional torus $$\mathbb {T}^n$$ , $$n \ge 1$$ . Here we analyze the solutions to these problems, studying their regularity and obtaining estimates of them. The main tools we use is the toroidal Fourier transform, together with Fourier series and a version of the Hardy-Littlewood inequality, applied to our case of the n-dimensional torus $$\mathbb {T}^n$$ . We use this inequality to find an estimate of solutions to evolution problems.
PubDate: 2021-07-14

• Time–frequency analysis associated with the k-Hankel Gabor transform on
$${\mathbb {R}}^{d}$$ R d

Abstract: Abstract In this paper, we investigate the k-Hankel Gabor transform on $${\mathbb {R}}^{d}$$ in some problems of time–frequency analysis. Firstly, we present the main theorems of Harmonic analysis as Plancherel’s, Lieb’s and inversion formulas for this transform. Next, we formulate some novel uncertainty principles including the Heisenberg and logarithmic uncertainty principles, Benedick–Amrein–Berthier’s uncertainty principle, local uncertainty principles and Shapiro’s uncertainty principle. In sequel, we introduce the localization operators associated with the k-Hankel Gabor transform on $${\mathbb {R}}^{d}$$ and we develop corresponding theory. In particular we study their trace class properties and we prove that they are in the Schatten–von Neumann.
PubDate: 2021-07-01

• $$\psi$$ ψ -Mittag–Leffler pseudo-fractional operators

Abstract: Abstract In this paper we present new types of pseudo-fractional integral and derivatives on a semiring $$([a,b],\oplus ,\odot )$$ . These operators are called the $$\psi$$ -Riemann–Liouville–Mittag–Leffler pseudo-fractional integrals and derivatives and $$\psi$$ -Caputo–Mittag–Leffler pseudo-fractional derivatives. Some properties, like the semigroup law, composition relations between pseudo-fractional differentiation and pseudo-fractional integration operators, composition relations between pseudo-fractional derivatives, among others, are discussed. Finally, as an application, we proved two versions of the fundamental theorem of fractional calculus.
PubDate: 2021-06-29

• Mixed radial-angular integrability for rough maximal operators

Abstract: Abstract In this paper, we study the mixed radial-angular integrability for maximal operators related to a class of rough singular integrals along “polynomial curves". Under assuming that the kernel satisfies certain rather weak size condition on sphere, we obtain the boundedness of such maximal operators on the mixed radial-angular Lebesgue spaces. Meanwhile, on the corresponding vector-valued versions are also established.
PubDate: 2021-06-16

• FIOs with cusp singularities and open umbrellas

Abstract: Abstract We study the composition calculus of Fourier integral operators F, with Morin singularities. This composition calculus falls outside of the classical transverse or clean intersection calculus of FIOs and it is motivated by the inverse problems studied in Felea and Greenleaf (Math Res Lett 17(5):867–886, 2010) and Felea and Nolan (J Fourier Anal Appl 21(4):799–821, 2015). In this case, the normal operator $$F^*F$$ is an operator with the wave front set in $$\Delta \cup \Lambda$$ where $$\Lambda$$ is a singular canonical relation called an open umbrella. We show that the operator $$F^*F$$ has the same order on $$\Delta \setminus \Lambda$$ and on $$\Lambda \setminus \Delta$$ . This result is a generalization of the results obtained in Felea and Greenleaf (2010) and Felea and Nolan (2015) where the canonical relations have the fold/cusp and cusp/cusp singularities.
PubDate: 2021-06-15

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