Boundedness of sublinear operators on weighted Morrey spaces and applications

TL;DR

This paper investigates the boundedness of various sublinear operators on weighted Morrey spaces, establishing their properties and applications to regularity of solutions to elliptic equations with VMO coefficients.

Contribution

It provides new boundedness results for a broad class of harmonic analysis operators on weighted Morrey spaces and applies these to elliptic PDE regularity.

Findings

Boundedness of Hardy-Littlewood maximal operator on weighted Morrey spaces.

Boundedness of Calderón-Zygmund singular integral operators on these spaces.

Regularity results for solutions to elliptic equations with VMO coefficients.

Abstract

We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator, Calder\'{o}n-Zygmund singular integral operator, Bochner-Riesz means at the critical index, oscillatory singular operators, singular integral operators with oscillating kernels and so on. As applications, the regularity in weighted Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients are established.