Authors:Alexander V. Abanin; Pham Trong Tien Pages: 1 - 15 Abstract: Motivated by some recent results on the boundedness and dynamical properties of the differentiation and integration operators in weighted Banach spaces of holomorphic functions, we study conditions on weights that guarantee the compactness of these two operators in the corresponding weighted spaces. PubDate: 2018-01-01 DOI: 10.1007/s13348-016-0185-z Issue No:Vol. 69, No. 1 (2018)

Authors:E. M. Bonotto Pages: 17 - 24 Abstract: In this work, we introduce the concept of monotone impulsive dynamical systems. We exhibit sufficient conditions for a set to be Zhukovskij quasi stable in dissipative monotone impulsive systems. Also, some recursive properties as minimality and recurrence are related with monotone impulsive systems. PubDate: 2018-01-01 DOI: 10.1007/s13348-016-0186-y Issue No:Vol. 69, No. 1 (2018)

Authors:Ganga Ram Gautam; Jaydev Dabas Pages: 25 - 37 Abstract: In this research article, we establish the existence results of mild solutions for semi-linear impulsive neutral fractional order integro-differential equations with state dependent delay subject to nonlocal initial condition by applying well known classical fixed point theorems. At last, we present an example of partial derivative to illuminate the results. PubDate: 2018-01-01 DOI: 10.1007/s13348-016-0189-8 Issue No:Vol. 69, No. 1 (2018)

Authors:Alessandra Bernardi; Joachim Jelisiejew; Pedro Macias Marques; Kristian Ranestad Pages: 39 - 64 Abstract: Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur. PubDate: 2018-01-01 DOI: 10.1007/s13348-016-0190-2 Issue No:Vol. 69, No. 1 (2018)

Authors:J. J. Nuño-Ballesteros; B. Oréfice-Okamoto; J. N. Tomazella Pages: 65 - 81 Abstract: Let (X, 0) be an ICIS of dimension 2 and let \(f:(X,0)\rightarrow (\mathbb C^2,0)\) be a map germ with an isolated instability. We look at the invariants that appear when \(X_s\) is a smoothing of (X, 0) and \(f_s:X_s\rightarrow B_\epsilon \) is a stabilization of f. We find relations between these invariants and also give necessary and sufficient conditions for a 1-parameter family to be Whitney equisingular. As an application, we show that a family \((X_t,0)\) is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant with respect to t. PubDate: 2018-01-01 DOI: 10.1007/s13348-017-0194-6 Issue No:Vol. 69, No. 1 (2018)

Authors:José Ángel Peláez; Daniel Seco Pages: 83 - 105 Abstract: Let \(\mathcal {D}_v\) denote the Dirichlet type space in the unit disc induced by a radial weight v for which \(\widehat{v}(r)=\int _r^1 v(s)\,\text {d}s\) satisfies the doubling property \(\int _r^1 v(s)\,\text {d}s\le C \int _{\frac{1+r}{2}}^1 v(s)\,\text {d}s.\) In this paper, we characterize the Schatten classes \(S_p(\mathcal {D}_v)\) of the generalized Hilbert operators $$\begin{aligned} \mathcal {H}_g(f)(z)=\int _0^1f(t)g'(tz)\,\text {d}t \end{aligned}$$ acting on \(\mathcal {D}_v\) , where v satisfies certain Muckenhoupt type conditions. For \(p\ge 1\) , it is proved that \(\mathcal {H}_{g}\in S_p(\mathcal {D}_v)\) if and only if $$\begin{aligned} \int _0^1 \left( (1-r)\int _{-\pi }^\pi g'(r\text {e}^{i\theta }) ^2\,\text {d}\theta \right) ^{\frac{p}{2}}\frac{{\text {d}}r}{1-r} <\infty . \end{aligned}$$ . PubDate: 2018-01-01 DOI: 10.1007/s13348-017-0195-5 Issue No:Vol. 69, No. 1 (2018)

Authors:Paolo Mantero; Jason McCullough Pages: 107 - 130 Abstract: Let S be a polynomial ring over an algebraically closed field k. Let x and y denote linearly independent linear forms in S so that \({\mathfrak {p}}= (x,y)\) is a height two prime ideal. This paper concerns the structure of \({\mathfrak {p}}\) -primary ideals in S. Huneke, Seceleanu, and the authors showed that for \(e \ge 3\) , there are infinitely many pairwise non-isomorphic \({\mathfrak {p}}\) -primary ideals of multiplicity e. However, we show that for \(e \le 4\) there is a finite characterization of the linear, quadric and cubic generators of all such \({\mathfrak {p}}\) -primary ideals. We apply our results to improve bounds on the projective dimension of ideals generated by three cubic forms. PubDate: 2018-01-01 DOI: 10.1007/s13348-017-0196-4 Issue No:Vol. 69, No. 1 (2018)

Authors:Sonia Brivio Pages: 131 - 150 Abstract: Let E be a stable vector bundle of rank r and slope \(2g-1\) on a smooth irreducible complex projective curve C of genus \(g \ge 3\) . In this paper we show a relation between theta divisor \(\Theta _E\) and the geometry of the tautological model \(P_E\) of E. In particular, we prove that for \(r > g-1\) , if C is a Petri curve and E is general in its moduli space then \(\Theta _E\) defines an irreducible component of the variety parametrizing \((g-2)\) -linear spaces which are g-secant to the tautological model \(P_E\) . Conversely, for a stable, \((g-2)\) -very ample vector bundle E, the existence of an irreducible non special component of dimension \(g-1\) of the above variety implies that E admits theta divisor. PubDate: 2018-01-01 DOI: 10.1007/s13348-017-0198-2 Issue No:Vol. 69, No. 1 (2018)

Authors:Robert Kesler; Michael T. Lacey Abstract: For \( 0< \lambda < \frac{1}{2}\) , let \( B _{\lambda }\) be the Bochner–Riesz multiplier of index \( \lambda \) on the plane. Associated to this multiplier is the critical index \(1< p_ \lambda = \frac{4}{3+2 \lambda } < \frac{4}{3}\) . We prove a sparse bound for \( B _{\lambda }\) with indices \( (p_ \lambda , q)\) , where \( p_ \lambda '< q < 4\) . This is a further quantification of the endpoint weak \(L^{p_ \lambda }\) boundedness of \( B _{\lambda }\) , due to Seeger. Indeed, the sparse bound immediately implies new endpoint weighted weak type estimates for weights in \( A_1 \cap RH _{\rho }\) , where \( \rho > \frac{4}{4 - 3 p _{\lambda }}\) . PubDate: 2018-01-27 DOI: 10.1007/s13348-018-0214-1

Authors:Takanobu Hara Abstract: In this note, we give a new proof of Wolff potential estimates for Cheeger p-superharmonic functions on metric measure spaces given by Björn et al. (J Anal Math 85:339–369, 2001). Also, we extend the estimate to Poisson type equations with signed data. PubDate: 2018-01-25 DOI: 10.1007/s13348-018-0213-2

Authors:M. Emilia Alonso; Henri Lombardi Pages: 419 - 432 Abstract: In this paper we prove what we call Local Bézout Theorem (Theorem 3.7). It is a formal abstract algebraic version, in the frame of Henselian rings and \(\mathfrak {m}\) -adic topology, of a well known theorem in the analytic complex case. This classical theorem says that, given an isolated point of multiplicity r as a zero of a local complete intersection, after deforming the coefficients of these equations we find in a sufficiently small neighborhood of this point exactly r isolated zeroes counted with multiplicities. Our main tools are, first the border bases [11], which turned out to be an efficient computational tool to deal with deformations of algebras. Second we use an important result of de Smit and Lenstra [7], for which there exists a constructive proof in [13]. Using these tools we find a very simple proof of our theorem, which seems new in the classical literature. PubDate: 2017-09-01 DOI: 10.1007/s13348-016-0184-0 Issue No:Vol. 68, No. 3 (2017)

Authors:Ruxi Shi Abstract: An oscillating sequence of order d is defined by the linearly disjointness from all \(\{e^{2\pi i P(n)} \}_{n=1}^{\infty }\) for all real polynomials P of degree smaller or equal to d. A fully oscillating sequence is defined to be an oscillating sequence of all orders. In this paper, we give several equivalent definitions of such sequences in terms of their disjointness from different dynamical systems on tori. PubDate: 2017-12-19 DOI: 10.1007/s13348-017-0211-9

Authors:Fumi-Yuki Maeda; Yoshihiro Mizuta; Tetsu Shimomura Abstract: Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a \(C^1\) -function on \({\mathbb R}^N{\setminus } \{0\}\) which vanishes outside the unit ball. PubDate: 2017-11-29 DOI: 10.1007/s13348-017-0210-x

Authors:Lisa Nicklasson Abstract: In this paper we classify the monomial complete intersections, in two variables, and of positive characteristic, which has the strong Lefschetz property. Together with known results, this gives a complete classification of the monomial complete intersections with the strong Lefschetz property. PubDate: 2017-11-09 DOI: 10.1007/s13348-017-0209-3

Authors:H. Al-Qassem; L. Cheng; Y. Pan Abstract: We study the \(L^{p}\) boundedness of certain classes of generalized Littlewood–Paley functions \(\mathcal{S}_{\Phi }^{(\lambda )}(f)\) . We obtain \(L^{p}\) estimates of \(\mathcal{S}_{\Phi }^{(\lambda )}(f)\) with sharp range of p and under optimal conditions on \(\Phi \) . By using these estimates along with an extrapolation argument we obtain some new and improved results on generalized Littlewood–Paley functions. The approach in proving our results is mainly based on proving vector-valued inequalities and in turn the proof of our results (in the case \(\lambda =2)\) provides us with alternative proofs of the results obtained by Duoandikoetxea as his approach is based on proving certain weighted norm inequalities. PubDate: 2017-10-24 DOI: 10.1007/s13348-017-0208-4

Authors:Kerboua Mourad; Ellaggoune Fateh; Dumitru Baleanu Abstract: This paper investigates the approximate controllability for Sobolev type stochastic perturbed control systems of fractional order with fractional Brownian motion and Sobolev fractional stochastic nonlocal conditions in a Hilbert space, A new set of sufficient conditions are established by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach’s fixed point theorem. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory. PubDate: 2017-10-20 DOI: 10.1007/s13348-017-0207-5

Authors:Giorgio Ottaviani; Alicia Tocino Abstract: In the tensor space \({{\mathrm {Sym}}}^d \mathbb {R}^2\) of binary forms we study the best rank k approximation problem. The critical points of the best rank 1 approximation problem are the eigenvectors and it is known that they span a hyperplane. We prove that the critical points of the best rank k approximation problem lie in the same hyperplane. As a consequence, every binary form may be written as linear combination of its critical rank 1 tensors, which extends the Spectral Theorem from quadratic forms to binary forms of any degree. In the same vein, also the best rank k approximation may be written as a linear combination of the critical rank 1 tensors, which extends the Eckart–Young theorem from matrices to binary forms. PubDate: 2017-10-11 DOI: 10.1007/s13348-017-0206-6

Authors:Angela A. Albanese; José Bonet; Werner J. Ricker Abstract: The spectrum of the Cesàro operator \(\mathsf {C}\) , which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fréchet or (LB) spaces of analytic functions on the open unit disc, is completely determined. It turns out that such spaces are always Schwartz but, with the exception of the Korenblum space, never nuclear. Some consequences concerning the mean ergodicity of \(\mathsf {C}\) are deduced. PubDate: 2017-09-26 DOI: 10.1007/s13348-017-0205-7

Authors:S. A. Seyed Fakhari; S. Yassemi Abstract: Let G be a graph with n vertices, let \(S={\mathbb {K}}[x_1,\dots ,x_n]\) be the polynomial ring in n variables over a field \({\mathbb {K}}\) and let I(G) denote the edge ideal of G. For every collection \({\mathcal {H}}\) of connected graphs with \(K_2\in {\mathcal {H}}\) , we introduce the notions of \({{\mathrm{ind-match}}}_{{\mathcal {H}}}(G)\) and \({{\mathrm{min-match}}}_{{\mathcal {H}}}(G)\) . It will be proved that the inequalities \({{\mathrm{ind-match}}}_{\{K_2, C_5\}}(G)\le \mathrm{reg}(S/I(G))\le {{\mathrm{min-match}}}_{\{K_2, C_5\}}(G)\) are true. Moreover, we show that if G is a Cohen–Macaulay graph with girth at least five, then \(\mathrm{reg}(S/I(G))={{\mathrm{ind-match}}}_{\{K_2, C_5\}}(G)\) . Furthermore, we prove that if G is a paw-free and doubly Cohen–Macaulay graph, then \(\mathrm{reg}(S/I(G))={{\mathrm{ind-match}}}_{\{K_2, C_5\}}(G)\) if and only if every connected component of G is either a complete graph or a 5-cycle graph. Among other results, we show that for every doubly Cohen–Macaulay simplicial complex, the equality \(\mathrm{reg}({\mathbb {K}}[\Delta ])=\mathrm{dim}({\mathbb {K}}[\Delta ])\) holds. PubDate: 2017-09-19 DOI: 10.1007/s13348-017-0204-8

Authors:Paul Hagelstein; Ioannis Parissis; Olli Saari Abstract: Let \(A_\infty ^+\) denote the class of one-sided Muckenhoupt weights, namely all the weights w for which \(\mathsf {M}^+:L^p(w)\rightarrow L^{p,\infty }(w)\) for some \(p>1\) , where \(\mathsf {M}^+\) is the forward Hardy–Littlewood maximal operator. We show that \(w\in A_\infty ^+\) if and only if there exist numerical constants \(\gamma \in (0,1)\) and \(c>0\) such that $$\begin{aligned} w(\{x \in \mathbb {R} : \, \mathsf {M}^+ \mathbf 1 _E (x)>\gamma \})\le cw(E) \end{aligned}$$ for all measurable sets \(E\subset \mathbb R\) . Furthermore, letting $$\begin{aligned} \mathsf {C_w ^+}(\alpha ){:}{=}\sup _{0<w(E)<+\infty } \frac{1}{w(E)} w(\{x\in \mathbb R:\,\mathsf {M}^+ \mathbf 1 _E(x)>\alpha \}) \end{aligned}$$ we show that for all \(w\in A_\infty ^+\) we have the asymptotic estimate \(\mathsf {C_w ^+}(\alpha )-1\lesssim (1-\alpha )^\frac{1}{c[w]_{A_\infty ^+}}\) for \(\alpha \) sufficiently close to 1 and \(c>0\) a numerical constant, and that this estimate is best possible. We also show that the reverse Hölder inequality for one-sided Muckenhoupt weights, previously proved by Martín-Reyes and de la Torre, is sharp, thus providing a quantitative equivalent definition of \(A_\infty ^+\) . Our methods also allow us to show that a weight \(w\in A_\infty ^+\) satisfies \(w\in A_p ^+\) for all \(p>e^{c[w]_{A_\infty ^+}}\) . PubDate: 2017-06-17 DOI: 10.1007/s13348-017-0201-y