Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness

The spaces and introduced by Ayd?n and Ba?ar [C. Ayd?n, F. Ba?ar, Some new difference sequence spaces, Appl. Math. Comput. 157 (3) (2004) 677-693] can be considered as the matrix domains of a triangle in the sets of all sequences that are summable to zero, summable, and bounded by the Cesàro method of order 1. Here we define the sets of sequences which are the matrix domains of that triangle in the sets of all sequences that are summable, summable to zero, or bounded by the strong Cesàro method of order 1 with index p?1. We determine the β-duals of the new spaces and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.     

Fractional integrals on weighted Hardy spaces

In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to .     

Bounded Toeplitz products on the weighted Bergman spaces of the unit ball

Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved.     

Rearrangements of functions on totally disconnected groups

A result of B.B. Wells Jr. claims that every complex valued continuous function on the compact ring of p-adic integers has a rearrangement which belongs to a certain class (W) of functions having absolutely convergent Fourier series. We point out that this is not the case since every real valued function from (W) has Lebesgue null range. On the other hand we prove the existence of a rearrangement with absolutely convergent Fourier series for every continuous real valued function on and on some other compact metric totally disconnected Abelian groups. We leave open if the same holds for all continuous complex valued functions on .     

q-Differential operator identities and applications

In this paper, we construct a new q-exponential operator and obtain some operator identities. Using these operator identities, we give a formal extension of Jackson's transformation formula. A formal extension of Bailey's summation and an extension of the Sears terminating balanced transformation formula are also derived by our operator method. In addition, we also derive several interesting a formal extensions involving multiple sum about three terms of Sears transformation formula and Heine's transformation formula.     

Banach frames for multivariate α-modulation spaces

The α-modulation spaces , α∈[0,1], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Riesz sequences based on tensor products of univariate brushlet functions, which simplifies the analysis of the full frame. We show that the multivariate α-modulation spaces can be completely characterized by the Banach frames constructed.     

A note on nice operators

In this note, we characterize nice operators in a class of Banach spaces, which includes spaces and L₁(μ), as those operators that preserve extreme points.     

Generalized sampling in shift-invariant spaces with multiple stable generators

The aim of this paper is to derive stable generalized sampling in a shift-invariant space with ? stable generators. This is done in the light of the theory of frames in the product Hilbert space (? times). The generalized samples are expressed as the frame coefficients of an appropriate function in with respect to some particular frame in . Since any multiply stable generated shift-invariant space is the image of by means of a bounded invertible operator, the generalized sampling is obtained from some dual frame expansions in . An example in the setting of the Hermite cubic splines is exhibited.     

Continuity and Schatten-von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

In this paper we investigate Hankel operators with anti-holomorphic symbols ∈L²(C,m|z|), where are general Fock spaces. We will show that is not continuous if the corresponding symbol is not a polynomial . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials we will give a complete characterization of the Schatten-von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators are in the Schatten-von Neumann p-class iff p>2m/(m−2k); and in case 2k?m they are not in the Schatten-von Neumann p-class.     

Transference of H-multipliers and their maximal functions on product domains

The aim of this paper is to establish de Leeuw type [K. de Leeuw, Ann. of Math. 81 (1965) 364-379] and Kenig-Tomas type [C.E. Kenig, P.A. Tomas, Studia Math. 68 (1989) 79-83] transference theorems for multipliers and maximal operators defined by multipliers on the multi-parameter Hardy spaces and , where 0<p?1, and . As an application, the restriction of multipliers and maximal operators defined by multipliers to lower dimensional spaces are considered.     

Global minimum and orthogonality in C1-classes

In this paper we characterize the global minimum of an arbitrary function defined on a Banach space, in terms of a new concept of derivatives adapted for our case from a recent work due to D.J. Keckic (J. Operator Theory, submitted for publication). Using these results we establish several new characterizations of the global minimum of the map defined by F_ψ(X)=‖ψ(X)‖₁, where is a map defined by ψ(X)=S+φ(X) and φ:B(H)→B(H) is a linear map, S∈C₁, and . Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators.     

On some iterated weighted spaces

It is proved that the Hörmander and spaces (Ω₁⊂Rn, Ω₂⊂Rm open sets, 1?p<∞, ki Beurling-Björck weights, k=k₁⊗k₂) are isomorphic whereas the iterated spaces and are not if 1<p≠q<∞. A similar result for weighted Lp-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: and are not isomorphic when 1<q≠2<∞.     

Analytic discs in the boundary and compactness of Hankel operators with essentially bounded symbols

We derive conditions for compactness of Hankel operators () with bounded, holomorphic symbols f for a large class of convex and bounded domains Ω with Ω⊆Dk.