Littlewood-Paley Operators on Morrey Spaces with Variable Exponent

Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...

Decomposition of Besov-Morrey Spaces

We establish a decomposition of Besov-Morrey spaces in terms of smooth “wavelets” obtained from a Littlewood-Paley partition of unity, or more generally molecules concentrated on dyadic cubes. We show that an expansion in atoms supported on dyadic cubes holds. We study atoms in Morrey spaces and prove a Littlewood-Paley theorem. Our results extend those of M. Frazier and B. Jawerth for Besov sp...

Some sharp inequalities for multilinear integral operators

In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.

Commutators of Littlewood-Paley Operators on the Generalized Morrey Space

Hardy Space Estimates for Littlewood-paley-stein Square Functions and Calderón-zygmund Operators

In this work, we give new sufficient conditions for Littlewood-Paley-Stein square function and necessary and sufficient conditions for a Calderón-Zygmund operator to be bounded on Hardy spaces H p with indices smaller than 1. New Carleson measure type conditions are defined for Littlewood-Paley-Stein operators, and the authors show that they are sufficient for the associated square function to ...