Characterizations for multilinear fractional maximal and integral operators and their commutators on generalized weighted Morrey spaces and applications

TL;DR

This paper investigates the boundedness of multilinear fractional maximal and integral operators and their commutators on generalized weighted Morrey spaces, providing characterizations, applications to Besov-Morrey spaces, and estimates for the sub-Laplacian.

Contribution

It introduces new characterizations for the boundedness of multilinear fractional operators and their commutators on generalized weighted Morrey spaces, extending previous results.

Findings

Established boundedness of multilinear fractional maximal operators.

Proved boundedness of multilinear fractional integral operators on generalized weighted Besov-Morrey spaces.

Derived embedding theorems and a priori estimates for the sub-Laplacian.

Abstract

This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator. Moreover, we show that two different characterizations for the boundedness of multilinear fractional maximal operators and their commutators on generalized weighted Morrey spaces under different conditions. As some inportant applications, we give the boundedness of multilinear fractional integral operator on generalized weighted Besov-Morrey spaces and also obtain two embedding theorems as well as apriori estimates for the sub-Laplacian $\mathcal L$.