Endpoint Estimates for N-dimensional Hardy Operators and Their Commutators

TL;DR

This paper establishes the boundedness of N-dimensional Hardy operators from Hardy spaces to Lebesgue spaces and explores endpoint estimates for their commutators with BMO functions.

Contribution

It provides new endpoint estimates for commutators of Hardy operators with BMO functions in higher dimensions, extending previous results.

Findings

Hardy operator is bounded from Hardy to Lebesgue spaces in N dimensions.

Endpoint estimates are obtained for commutators with BMO functions.

Results extend the understanding of Hardy operator behavior in higher-dimensional analysis.

Abstract

In this paper, it is proved that the higher dimensional Hardy operator is bounded from Hardy space to Lebesgue space. The endpoint estimate for the commutator generated by Hardy operator and (central) BMO function is also discussed.