The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

New Characterizations of the Dual Spaces of Hardy-amalgam Spaces

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0<q,p<∞),we give a characterization of their dual spaces whenever 0<q≤1 and q≤p<∞.Moreover,when 0<q≤p≤1,these characterizations coincide with those obtained in our earlier papers.

Some Estimates forθ-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

In this paper,we first introduce some new kinds of weighted amalgam spaces.Then we discuss the strong type and weak type estimates for a class of Calderόn-Zygmund type operators Tθin these new weighted spaces.Furthermore,the strong type estimate and endpoint estimate of linear commutators[b,Tθ]formed by b and Tθare established.Also we study related problems about two-weight,weak type inequalities for Tθand[b,Tθ]in the weighted amalgam spaces and give some results.

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.

Restricted Summability of Fourier Transforms and Local Hardy Spaces

A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W（hp, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.

Mapping Properties of Certain Oscillatory Integrals on Modulation Spaces

Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtds on modulation spaces, where Q^2 = [0, 1] × [0, 1] is the unit square in two dimensions.

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^(con)_((p,q,s)) over R^(n) or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over R^(n) or a given cube of R^(n) with finite side length.Furthermore, some VMO-H^(1)-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.