The multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces

TL;DR

This paper establishes the boundedness of multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, providing new insights into their behavior and related weak-type estimates.

Contribution

It introduces the boundedness results for multilinear Littlewood-Paley operators and their commutators on weighted Morrey spaces, including new weak-type $L ext{log}L$ estimates.

Findings

Boundedness of multilinear Littlewood-Paley square operators on weighted Morrey spaces.

Boundedness and weak-type $L ext{log}L$ estimates for commutators of multilinear Littlewood-Paley g-functions.

Extension of results to multilinear Marcinkiewicz integrals.

Abstract

In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear Littlewood-Paley g-functions and multilinear Marcinkiewicz integrals on weighted Morrey spaces in the form of corollaries.