New weighted multilinear operators and commutators of Hardy-Ces\`aro type

TL;DR

This paper introduces a broad class of weighted multilinear Hardy-Ces operators acting on Lebesgue and Morrey spaces, establishes their sharp bounds, and characterizes the boundedness of their commutators with symbols in central BMO space.

Contribution

It extends existing results by defining new weighted multilinear operators, deriving their sharp bounds, and providing necessary and sufficient conditions for the boundedness of their commutators.

Findings

Established sharp bounds for the new operators.

Derived conditions for boundedness of commutators.

Extended known results on multilinear Hardy operators.

Abstract

A general class of weighted multilinear Hardy-Ces\`aro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Ces\`aro operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.