Boundedness of some sublinear operators in weighted Herz-type 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.

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces

Weighted Anisotropic Product Hardy Spaces and Boundedness of Sublinear Operators

Let A1 and A2 be expansive dilations, respectively, on R n and R. Let ~ A ≡ (A1, A2) and Ap( ~ A) be the class of product Muckenhoupt weights on R × R for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ Ap( ~ A), the authors characterize the weighted Lebesgue space L w (R × R) via the anisotropic Lusin-area function associated with ~ A. When p ∈ (0, 1], w ∈ A∞( ~ A), the authors introduce the weighted anis...

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...

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...