On a two-weight criteria for multidimensional Hardy type operator in $p$-convex Banach function spaces and some application

TL;DR

This paper establishes two-weight criteria for the boundedness of multidimensional Hardy type and geometric mean operators between weighted Lebesgue and Banach function spaces, with applications to Musielak-Orlicz spaces.

Contribution

It introduces new two-weight criteria for Hardy type operators in p-convex Banach spaces and applies these results to geometric mean and sublinear operators.

Findings

Derived two-weight criteria for Hardy type operators.

Established conditions for boundedness of geometric mean operators.

Provided sufficient conditions for sublinear operators in Musielak-Orlicz spaces.

Abstract

The main goal of this paper is to prove a two-weight criteria for multidimensio-nal Hardy type operator from weighted Lebesgue spaces into $p$-convex weighted Banach function spaces. Analogously problem for the dual operator is considered. As application we prove a two-weight criteria for boundedness of multidimensional geometric mean operator and sufficient condition on the weights for boundedness of certain sublinear operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces.