Average Operators on Rectangular Herz Spaces

Bilinear Operators on Herz-type Hardy Spaces

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

Weighted Multilinear Hardy Operators on Herz Type Spaces

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained resul...

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces

Endpoint boundedness for multilinear integral operators of some sublinear operators on Herz and Herz type Hardy spaces

The purpose of this paper is to study the endpoint boundedness properties of some multilinear operators related to certain integral operators on Herz and Herz type Hardy Spaces. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

Vector-valued Inequalities on Herz Spaces and Characterizations of Herz–sobolev Spaces with Variable Exponent

The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...