-
Duality for vector-valued Bergman–Orlicz spaces and little Hankel operators between vector-valued Bergman–Orlicz spaces on the unit ball Anal. Math. (IF 0.7) Pub Date : 2024-03-13
Abstract In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, \(h_b\) , with operator-valued symbols b, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball \(\mathbb{B}_n\)
-
Nonstationary matrix-valued multiresolution analysis from the extended affine group Anal. Math. (IF 0.7) Pub Date : 2024-02-26 D. Jindal, L. K. Vashisht
We characterize scaling functions of nonstationary matrix-valued multiresolution analysis in the matrix-valued function space \(L^2(\mathbb{R}, \mathbb{C}^{l \times l})\), l is a natural number. This is inspired by the work of Novikov, Protasov and Skopina on nonstationary multiresolution analysis of the space \(L^2(\mathbb{R})\). Using a sequence of diagonal matrix-valued scaling functions in \(L^2(\mathbb{R}
-
Reaction-diffusion equations on metric graphs with edge noise Anal. Math. (IF 0.7) Pub Date : 2024-02-20 E. Sikolya
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily
-
Boundedness of the Hilbert Transform in Besov Spaces Anal. Math. (IF 0.7) Pub Date : 2023-11-15 E. P. Ushakova
Boundedness conditions are found for the Hilbert transform H in Besov spaces with Muckenhoupt weights. The operator H in this situation acts on subclasses of functions from Hardy spaces. The results are obtained by representing the Hilbert transform H via Riemann–Liouville operators of fractional integration on ℝ, on the norms of images and pre-images of which independent estimates are established
-
Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative Anal. Math. (IF 0.7) Pub Date : 2023-11-15 Z. Gong, J. Li, B. D. Wick
In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L2 spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.
-
Quasilinear PDEs, Interpolation Spaces and Hölderian mappings Anal. Math. (IF 0.7) Pub Date : 2023-11-15 I. Ahmed, A. Fiorenza, M. R. Formica, A. Gogatishvili, A. El Hamidi, J. M. Rakotoson
As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-Hölderian mappings between normed spaces, by studying the action of the mappings on K-functionals and between interpolation spaces with logarithm functions. We apply these results to obtain some regularity results on the gradient of the solutions to quasilinear equations of the form $$-\text{div}(\widehat{a}(\nabla
-
Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators Anal. Math. (IF 0.7) Pub Date : 2023-10-28 H. Rafeiro, S. Samko, S. Umarkhadzhiev
The approach to “locally” aggrandize Lebesgue spaces, previously suggested by the authors and based on the notion of “aggrandizer”, is combined with the usual “global” aggrandization. We study properties of such spaces including embeddings, dependence of the choice of the aggrandizer and, in particular, we discuss the question when these spaces are not new, coinciding with globally aggrandized spaces
-
Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces Anal. Math. (IF 0.7) Pub Date : 2023-10-09 V. I. Kolyada
The paper is dedicated to the study of embeddings of the anisotropic Besov spaces \(B_{p,{\theta _1}, \ldots ,{\theta _n}}^{{\beta _1}, \ldots ,{\beta _n}}\) (ℝn) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents βk tend to 1 (βk < 1). In particular, these results give an extension of the estimate proved by Bourgain, Brezis, and Mironescu
-
Nuclear and Compact Embeddings in Function Spaces of Generalised Smoothness Anal. Math. (IF 0.7) Pub Date : 2023-10-09 D. D. Haroske, H.-G. Leopold, S. D. Moura, L. Skrzypczak
We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain Ω ⊂ ℝd. This covers, in particular, the well-known situation for spaces of Besov and Triebel–Lizorkin spaces defined on bounded domains as well as some first results for function spaces of logarithmic smoothness. In addition, we provide some new, more general approach to compact embeddings
-
Two Weighted Norm Inequalities of Potential Type Operator on Herz Spaces Anal. Math. (IF 0.7) Pub Date : 2023-10-09 K.-P. Ho, T.-L. Yee
We extend the two weighted norm inequalities for the potential type operators to Herz spaces. As an application of this result, we have the two weighted norm inequalities of the fractional integral operators on Herz spaces.
-
Diversity of Lorentz-Zygmund Spaces of Operators Defined by Approximation Numbers Anal. Math. (IF 0.7) Pub Date : 2023-10-09 F. Cobos, T. Kühn
We prove the following dichotomy for the spaces ℒ (a)p,q,α (X, Y) of all operators T ∈ ℒ(X, Y) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces ℓp,q(log ℓ)α: If X and Y are infinite-dimensional Banach spaces, then the spaces ℒ (a)p,q,α (X, Y) with 0 < p < ∞, 0 < q ≤ ∞ and α ∈ ℝ are all different from each other, but otherwise, if X or Y are finite-dimensional, they are all
-
Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties Anal. Math. (IF 0.7) Pub Date : 2023-09-06 T. Beberok
In this paper we introduce a generalization to compact subsets of certain algebraic varieties of the classical Markov inequality on the derivatives of a polynomial in terms of its own values. We also introduce an extension to such sets of a local form of the classical Markov inequality, and show the equivalence of introduced Markov and local Markov inequalities.
-
Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density Anal. Math. (IF 0.7) Pub Date : 2023-09-06 S. Yu. Favorov
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sums of derivatives of generalized lattice Dirac combs. These theorems are derived from properties of families of discretely supported measures and almost periodic distributions.
-
Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges Anal. Math. (IF 0.7) Pub Date : 2023-09-06 Z. Douzi, B. Selmi, Z. Yuan
The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind of outer regularity in a general metric space X. We give also some conditions on the Hewitt–Stromberg pre-measures with respect to the gauge such that the Hewitt–Stromberg measures have an almost inner regularity on a complete separable metric space X
-
On the Commutativity of Closed Symmetric Operators Anal. Math. (IF 0.7) Pub Date : 2023-09-06 S. Dehimi, M. H. Mortad, A. Bachir
In this paper, we mainly show that if a product AB (or BA) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A. Certain generalizations and consequences are also presented.
-
On Meromorphic Solutions of Nonlinear Complex Differential Equations Anal. Math. (IF 0.7) Pub Date : 2023-09-06 J.-F. Chen, Y.-Y. Feng
By utilizing Nevanlinna theory of meromorphic functions, we characterize meromorphic solutions of the following nonlinear differential equation of the form $${f^n}{f^\prime } + P(z,f,{f^\prime }, \ldots ,{f^{(t)}}) = {P_1}{e^{{\alpha _1}z}} + {P_2}{e^{{\alpha _2}z}} + \cdots + {P_m}{e^{{\alpha _m}z}},$$ where n ≥ 3, t ≥ 0 and m ≥ 1 are integers, n ≥ m, P(z, f, f′, …, f(t)) is a differential polynomial
-
Stability of $${\cal A}{\cal N}$$ -Operators under Functional Calculus Anal. Math. (IF 0.7) Pub Date : 2023-09-06 G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki
In this note we discuss absolutely norm attaining property (\({\cal A}{\cal N}\)-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the \({\cal A}{\cal N}\)-property under the functional calculus. As a consequence we discuss the operator mean of positive \({\cal A}{\cal N}\)-operators
-
Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G) Anal. Math. (IF 0.7) Pub Date : 2023-09-06 S. Soltani Renani, Z. Yari
Let G be a locally compact group, \({\cal B}({L^2}(G))\) be the space of all bounded linear operators on L2(G), and \(({\cal T}({L^2}(G)), \ast)\) be the Banach algebra of trace class operators on L2(G). In this paper, we focus on some Banach right submodules of \({\cal B}({L^2}(G))\) over the convolution algebras \(({\cal T}({L^2}(G)), \ast)\) and (L1(G),*). We will see that if the locally compact
-
A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps Anal. Math. (IF 0.7) Pub Date : 2023-09-06 A. Ranjbar-Motlagh
This article describes the surjective linear isometries between spaces of p-times differentiable maps from a domain of the Euclidean space into a certain Banach space.
-
On the Edrei–Goldberg–Ostrovskii Theorem for Minimal Surfaces Anal. Math. (IF 0.7) Pub Date : 2023-09-06 A. Kowalski, I. I. Marchenko
This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s T*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.
-
Completion Procedures in Measure Theory Anal. Math. (IF 0.7) Pub Date : 2023-09-06 A. G. Smirnov, M. S. Smirnov
We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content μ. With every such ring \({\cal N}\), an extension of μ is naturally associated which is called the \({\cal N}\)-completion of μ. The \({\cal N}\)-completion operation comprises
-
Global Stein Theorem on Hardy Spaces Anal. Math. (IF 0.7) Pub Date : 2023-09-05 A. Bonami, S. Grellier, B. F. Sehba
Let f be an integrable function which has integral 0 on ℝn. What is the largest condition on ❘ f ❘ that guarantees that f is in the Hardy space \({{\cal H}^1}\) (ℝn)? When f is compactly supported, it is well-known that the largest condition on ❘f❘ is the fact that ❘f❘ ∈ L log L(ℝn). We consider the same kind of problem here, but without any condition on the support. We do so for \({{\cal H}^1}\) (ℝn)
-
A Note on the Maximal Operator on Weighted Morrey Spaces Anal. Math. (IF 0.7) Pub Date : 2023-09-05 A. K. Lerner
In this paper we consider weighted Morrey spaces \({\cal M}_{\lambda ,{\cal F}}^p(w)\) adapted to a family of cubes \({\cal F}\), with the norm $$\Vert f\Vert{_{{\cal M}_{\lambda ,{\cal F}}^p(w)}}: = \mathop {\sup }\limits_{Q \in {\cal F}} {\left( {{1 \over {|Q{|^\lambda }}}\int_Q {|f{|^p}w} } \right)^{1/p}},$$ and the question we deal with is whether a Muckenhoupt-type condition characterizes the
-
Weighted Weak Type Mixed Φ-Inequalities for Martingale Maximal Operator Anal. Math. (IF 0.7) Pub Date : 2023-09-05 Y. Ren
In this article, some necessary and sufficient conditions are shown for weighted weak type mixed Φ-inequality and weighted extra-weak type mixed Φ-inequality for martingale maximal operator. The obtained results generalize some existing statements.
-
Building Blocks in Function Spaces Anal. Math. (IF 0.7) Pub Date : 2023-09-05 H. Triebel
The spaces A sp,q (ℝn)with A ∈ {B, F}, s ∈ ℝ and 0
-
The pointwise James type constant Anal. Math. (IF 0.7) Pub Date : 2023-06-08 M. A. Rincón-Villamizar
-
Weyl’s asymptotic formula for fractal Laplacians defined by a class of self-similar measures with overlaps Anal. Math. (IF 0.7) Pub Date : 2023-06-08 W. Tang, Z. Y. Wang
We observe that some self-similar measures that we call essentially of finite type satisfy countable measure type condition. We make use of this condition to set up a framework to obtain a precise analog of Weyl’s asymptotic formula for the eigenvalue counting function of Laplacians defined by measures, emphasizing on one-dimensional self-similar measures with overlaps. As an application of our result
-
Representing certain vector-valued function spaces as tensor products Anal. Math. (IF 0.7) Pub Date : 2023-06-08 M. Abtahi
Let E be a Banach space. For a topological space X, let \({{\cal C}_b}(X,E)\) be the space of all bounded continuous E-valued functions on X, and let \({{\cal C}_K}(X,E)\) be the subspace of \({{\cal C}_b}(X,E)\) consisting of all functions having a pre-compact image in E. We show that \({{\cal C}_K}(X,E)\) is isometrically isomorphic to the injective tensor product \({{\cal C}_b}(X){{\hat \otimes}_\varepsilon}E\)
-
Fermat and Malmquist type matrix differential equations Anal. Math. (IF 0.7) Pub Date : 2023-06-08 Y. X. Li, K. Liu, H. B. Si
The systems of nonlinear differential equations of certain types can be simplified to matrix forms. Two types of matrix differential equations will be considered in the paper, one is Fermat type matrix differential equation $$A{(z)^n} + A'{(z)^n} = E$$ where n = 2 and n = 3, another is Malmquist type matrix differential equation $$A'(z) = \alpha A{(z)^2} + \beta A(z) + \gamma E,$$ , where α (≠ 0),
-
The gaussian convolution and reproducing kernels associated with the Hankel multidimensional operator Anal. Math. (IF 0.7) Pub Date : 2023-06-08 B. Amri
We consider the Hankel multidimensional operator defined on]0, +∞[n by $${\Delta _\alpha} = \sum\limits_{j = 1}^n {\left({{{{\partial ^2}} \over {\partial x_j^2}} + {{2{\alpha _j} + 1} \over {{x_j}}}{\partial \over {\partial {x_j}}}} \right)} $$ where \(\alpha = ({\alpha _1},{\alpha _2}, \ldots ,{\alpha _n}) \in ] - {1 \over 2}, + \infty {[^n}\). We give the most important harmonic analysis results
-
μ-Hankel Operators on Compact Abelian Groups Anal. Math. (IF 0.7) Pub Date : 2023-04-19 A. Mirotin
(μ; ν)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, μ-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (μ; ν)-Hankel operators to the case of (non-separable in general) Hardy spaces over compact and connected Abelian groups. In this setting bounded (μ; ν)-Hankel
-
The Pseudoinverse of the Laplacian Matrix: Asymptotic Behavior of its Trace Anal. Math. (IF 0.7) Pub Date : 2023-04-19 F. Ecevit, C. Y. Yildirim
In this paper we are concerned with the asymptotic behavior of $${\rm{tr}}({\cal L}_{{\rm{sq}}}^ + ) = {1 \over 4}\sum\limits_{\matrix{{j,k = 0} \cr {(j,k) \ne (0,0)} \cr } }^{n - 1} {{1 \over {1 - {1 \over 2}(\cos {{2\pi j} \over n} + \cos {{2\pi k} \over n})}},} $$ the trace of the pseudoinverse of the Laplacian matrix related with the square lattice, as n → ∞. The method we developed for such sums
-
Uniform Distribution of Sequences and its Interplay with Functional Analysis Anal. Math. (IF 0.7) Pub Date : 2023-03-31 S. K. Mercourakis, G. Vassiliadis
In this paper we apply ideas from the theory of Uniform Distribution of sequences to Functional Analysis and then drawing inspiration from the consequent results, we study concepts and results in Uniform Distribution itself. so let E be a Banach space. then we prove: (a) If F is a bounded subset of E and \(x \in \overline {{\rm{co}}} (F)\) (= the closed convex hull of F), then there is a sequence (xn)
-
Non-Archimedean Banach Spaces of Universal Disposition Anal. Math. (IF 0.7) Pub Date : 2023-03-31 A. Kubzdela, C. Perez-Garcia
A space of universal disposition is a Banach space which has certain natural extension properties for isometric embeddings of Banach spaces belonging to a specific class. We study spaces of universal disposition for non-archimedean Banach spaces. In particular, we introduce the classification of non-archimedean Banach spaces depending on the cardinality of maximal orthogonal sets, which can be viewed
-
On Limiting Directions of Entire Solutions of Complex Differential-Difference Equations Anal. Math. (IF 0.7) Pub Date : 2023-03-31 H. X. Dai, J. Y. Qiao, T. B. Cao
In this article, we mainly obtain the measure of Julia limiting directions and transcendental directions of Jackson difference operators of non-trivial transcendental entire solutions for differential-difference equation \({f^n}(z) + \sum\limits_{k = 0}^n {{a_{{\lambda _k}}}(z){p_{{\lambda _k}}}(z,f) = h(z),} \) where \({p_{{\lambda _k}}}(z,f)\,\,\,(\lambda \in \mathbb{N})\) are distinct differential-difference
-
Poincaré Inequalities on Graphs Anal. Math. (IF 0.7) Pub Date : 2023-03-31 M. Levi, F. Santagati, A. Tabacco, M. Vallarino
Every graph of bounded degree endowed with the counting measure satisfies a local version of Lp-Poincaré inequality, p ∈ [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of Lp-Poincaré inequality, despite the fact that
-
On a Boundary Property of Blaschke Products Anal. Math. (IF 0.7) Pub Date : 2023-03-31 A. A. Danielyan, S. Pasias
A Blaschke product has no radial limits on a subset E of the unit circle T but has unrestricted limit at each point of T E if and only if E is a closed set of measure zero.
-
Mean Value Inequalities for the Digamma Function Anal. Math. (IF 0.7) Pub Date : 2023-03-01 H. Alzer, M. K. Kwong
Let ψ be the digamma function and let L(a,b) = (b − a)/log(b/a) be the logarithmic mean of a and b. We prove that the inequality $$\left( * \right)\,\,\,\,\,\,\,\,\,\,\,\,{\kern 1pt} \left( {b - a} \right)\psi \left( {\sqrt {ab} } \right) < \left( {L\left( {a,b} \right) - a} \right)\psi \left( a \right) + \left( {b - L\left( {a,b} \right)} \right)\psi \left( b \right)$$ holds for all real numbers a
-
Inverse-Closedness of the Subalgebra of Locally Nuclear Operators Anal. Math. (IF 0.7) Pub Date : 2023-02-28 E. Yu. Guseva, V. G. Kurbatov
Let X be a Banach space and T be a bounded linear operator acting in lp(ℤc,X), 1 ≤ p ≤ ∞. The operator T is called locally nuclear if it can be represented in the form $${(Tx)_k} = \sum\limits_{m \in {\mathbb{Z}^c}} {{b_{km}}} {x_{k - m}},\quad k \in {\mathbb{Z}^c},$$ where bkm: X → X are nuclear, $${\left\| {{b_{km}}} \right\|_{{\mathfrak{S}_1}}} \le {\beta _m},\quad k,m \in {\mathbb{Z}^c},$$ \(\
-
A Decay Estimate for the Fourier Transform of Certain Singular Measures in ℝ4 and Applications Anal. Math. (IF 0.7) Pub Date : 2023-02-28 T. Godoy, P. Rocha
We consider, for a class of functions φ: ℝ2 {0} → ℝ2 satisfying a nonisotropic homogeneity condition, the Fourier transform û of the Borel measure on ℝ4 defined by $$\mu \left(E \right) = \int_U {{\chi E}\left({x,\varphi \left(x \right)} \right)} \,dx$$ where E is a Borel set of ℝ4 and \(U = \left\{{\left({{t^{{\alpha _1}}},{t^{{\alpha _2}}}s} \right):c < s < d,\,\,0 < t < 1} \right\}\). The aim of
-
Spectral Eigenmatrix of the Planar Spectral Measures with Four Elements Anal. Math. (IF 0.7) Pub Date : 2023-02-28 S.-J. Li, W.-H. Ai
We consider the spectral eigenmatrix problem of the planar self-similar spectral measures μQ,D generated by $$Q = \left({\matrix{{2q} & 0 \cr 0 & {2q} \cr}} \right)\,\,\,{\rm{and}}\,\,\,D = \left\{{\left({\matrix{0 \cr 0 \cr}} \right),\left({\matrix{1 \cr 0 \cr}} \right),\left({\matrix{0 \cr 1 \cr}} \right),\left({\matrix{{- 1} \cr {- 1} \cr}} \right)} \right\},$$ where q ≥ 2 is an integer. For matrix
-
A Particular Family of Absolutely Monotone Functions and Relations to Branching Processes Anal. Math. (IF 0.7) Pub Date : 2023-02-28 M. Möhle
It is shown that the map z ↦ log(1 − c−1 log(1 − z)) is absolutely monotone on [0, 1) if and only if c ≥ 1. The proof is based on an integral representation for the associated Taylor coefficients and on one of Gautschi’s double inequalities for the quotient of two gamma functions. The result is used to verify that, for every c ≥ 1 and α ∈ (0, 1], the map z ↦ 1 − exp(c − c(1 − c−1 log(1 − z))α) is absolutely
-
On the Order and the Type of an Entire Function Anal. Math. (IF 0.7) Pub Date : 2023-02-28 E. Kallitsi, V. G. Papanicolaou, G. Smyrlis
In this short article we present some properties regarding the order and the type of an entire function.
-
Off-Diagonal two Weight Bumps for Fractional Sparse Operators Anal. Math. (IF 0.7) Pub Date : 2023-02-08 R. Rahm
In this paper, we continue some recent work on two weight boundedness of sparse operators to the “off-diagonal” setting. We use the new “entropy bumps” introduced in by Treil and Volberg and improved by Lacey and Spencer [11] and the “direct comparison bumps” introduced by Rahm and Spencer [23] and improved by Lerner [14]. Our results are “sharp” in the sense that they are sharp in various particular
-
Complex Linear Differential Equations with Solutions in Dirichlet—Morrey Spaces Anal. Math. (IF 0.7) Pub Date : 2023-02-08 Y. Sun, B. Liu, J. L. Liu
The nth derivative criterion for functions belonging to the Dirichlet—Morrey space \({\cal D}_p^\lambda \) is given in this paper. Furthermore, two sufficient conditions for coefficients of the complex linear differential equation $${f^{\left(n \right)}} + {A_{n - 1}}\left(z \right){f^{\left({n - 1} \right)}} + \cdots + {A_1}\left(z \right){f^\prime} + {A_0}\left(z \right)f = {A_n}\left(z \right)$$
-
The Growth of Meromorphic Solutions of a Class of Delay-Differential Equations Anal. Math. (IF 0.7) Pub Date : 2023-02-08 Z. Li, J. Zhang
We obtain necessary conditions for certain type of rational delay-differential equations to allow the existence of a non-rational meromorphic solution with hyper-order less than one. In addition, we give a further discussion of the coefficients of a delay-differential equation with fixed degree.
-
Composition Operators in Grand Lebesgue Spaces Anal. Math. (IF 0.7) Pub Date : 2023-02-08 A. Karapetyants, M. Lanza De Cristoforis
Let Ω be an open subset of ℝn of finite measure. Let f be a Borel measurable function from ℝ to ℝ. We prove necessary and sufficient conditions on f in order that the composite function Tf[g] = f o g belongs to the Grand Lebesgue space Lp),θ(Ω) whenever g belongs to Lp),θ (Ω). We also study continuity, uniform continuity, Hölder and Lipschitz continuity of the composition operator Tf[·] in Lp),θ(Ω)
-
The Double Layer Potential Operator on Hardy Spaces Anal. Math. (IF 0.7) Pub Date : 2023-02-08 Y. Komori-Furuya
Many studies have been done for one-dimensional Cauchy integral operator. We consider n-dimensional Cauchy integral operator for hypersurface, or we say, the double layer potential operator, and obtain the boundedness from Hp(Rn) to hp(Rn) (local Hardy space). For the proof we introduce Clifford valued Hardy spaces.
-
Asymptotics of Sums of Sine Series with Fractional Monotonicity Coefficients Anal. Math. (IF 0.7) Pub Date : 2023-01-23 M. I. Dyachenko, A. P. Solodov
We study the following question: which monotonicity order implies upper and lower estimates of the sum of a sine series \(g\left({{\boldsymbol{b}},x} \right) = \sum\nolimits_{k = 1}^\infty {{b_k}\sin \,kx} \) near zero in terms of the function \(v\left({{\boldsymbol{b}},x} \right) = x\sum\nolimits_{k = 1}^{[\pi /x]} {k{b_k}} \). Our results complete, on a qualitative level, the studies began by R.
-
The Hilbert Transform for Dunkl Differential Operators Associated to the Reflection Group ℤ2 Anal. Math. (IF 0.7) Pub Date : 2023-01-23 I. A. López P
The aim of this paper is to introduce the Dunkl-Hilbert transform Hk, with k ≥ 0, induced by the Dunkl differential operator and associated with the reflection group ℤ2. For this end, we establish that the Dunkl-Poisson kernel and the conjugate Dunkl-Poisson kernel satisfy the Cauchy-Riemann equations in the Dunkl context. We prove the continuity of Hk on Lp(wk) for 1 < p < ∞, where wk(x) = ∣x∣2k.
-
On the Inverse Poletsky Inequality in Metric Spaces and Prime Ends Anal. Math. (IF 0.7) Pub Date : 2023-01-23 E. Sevost’yanov
We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletsky inequality. It is proved that such mappings have a continuous extension to the boundary of the domain in terms of prime ends. Under some additional conditions, the families of such mappings are equicontinuous in the closure of the domain with respect to the space
-
The Property (D) and the Almost Limited Completely Continuous Operators Anal. Math. (IF 0.7) Pub Date : 2023-01-23 M. L. Lourenço, V. C. C. Miranda
In this paper, we study some geometric properties in Banach lattices and the class of almost limited completely continuous operators. For example, we study Banach lattices with property (d) and we give a new characterization of this property in terms of the solid hull of almost limited sets.
-
A Derivative-Free Characterization of the Weighted Besov Spaces Anal. Math. (IF 0.7) Pub Date : 2023-01-23 W. Pan, H. Wulan
We obtain a characterization of the weighted Besov space \({{\cal B}_K}\left(p \right)\) for a weight function K,0 < p < ∞, in terms of symmetric and derivative-free double integrals with the weight function K in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of \({{\cal Q}_K}\)
-
New Aspects of Universality of Hurwitz Zeta-Functions Anal. Math. (IF 0.7) Pub Date : 2023-01-23 A. Laurinčikas
We construct an absolutely convergent Dirichlet series connected to the classical Hurwitz zeta-function. The shifts of this function approximate analytic functions defined in the right-hand side of the critical strip.
-
Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings Anal. Math. (IF 0.7) Pub Date : 2022-12-20 M. I. Ganzburg
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements, and approximation on classes of elements. Second, we find sufficient conditions that imply limit relations between various sharp constants of approximation theory
-
Predual Spaces for the Space of (p, q)-Multipliers and Their Application in Stechkin’s Problem on Approximation of Differentiation Operators Anal. Math. (IF 0.7) Pub Date : 2022-12-20 V. V. Arestov
A. Figà-Talamanca and G. I. Gaudry proved (1967) that the space \({{\cal T}_{p,q}}\left( G \right)\) of bounded linear operators from the space Lp to the space Lq, 1 ≤ p ≤ q < ∞, on a locally compact Abelian group G that are translation invariant (more exactly, invariant with respect to the group operation) is a conjugate space for a space Ap,q(G), which they described constructively. Figà-Talamanca
-
On Iterated Discrete Hardy Type Inequalities for a Class of Matrix Operators Anal. Math. (IF 0.7) Pub Date : 2022-12-10 A. Kalybay, A. Temirkhanova, N. Zhangabergenova
In this paper, we discuss new iterated discrete inequalities of Hardy type involving matrix kernels. Under some conditions on matrix entries of the kernels, we establish weight characterizations of these inequalities.
-
Approximation in Variable Exponent Spaces and Growth of Norms of Trigonometric Polynomials Anal. Math. (IF 0.7) Pub Date : 2022-12-10 S. Volosivets
Using a variant of Nikol’skii—Stechkin inequality we investigate the approximation problems in Hölder type spaces connected with variable exponent spaces. Also, we estimate best approximations and moduli of smoothness of functions in variable exponent spaces by norm of derivatives of approximating polynomials in these spaces. As a consequence, we obtain a description of Hölder type spaces.
-
On the Corona Problem for Strongly Pseudoconvex Domains Anal. Math. (IF 0.7) Pub Date : 2022-11-29 A. Tikaradze
In this note we solve that the corona problem for strongly pseudoconvex domains under a certain assumption on the level sets of the corona data. This result settles a question of S. Krantz [4].
-
Approximate Continuity and Differentiability with Respect to Density Degree, An Application to BV and Sobolev Functions Anal. Math. (IF 0.7) Pub Date : 2022-11-29 S. Delladio
We define and discuss the pointwise notion of m-approximate continuity (differentiability) for functions \(f:A \subset {\mathbb{R}^n} \to \overline {\mathbb{R}} \), with m ≥ n. The function f is m-approximately continuous (differentiable) at x ∈ A if and only if there exists E ⊂ A such that x ∈ E, limr→0+ r−mℒn(Br(x) \ E) = 0 and f|E is continuous (differentiable) at x. For m = n this notion coincides