A characterization of weighted local Hardy spaces

TL;DR

This paper characterizes weighted local Hardy spaces using truncated Riesz transforms, extending previous results to a broader class of local weights.

Contribution

It introduces a new characterization of weighted local Hardy spaces with local weights via truncated Riesz transforms, generalizing prior work.

Findings

Established a new characterization of weighted local Hardy spaces

Extended the result of Bui to more general local weights

Provided tools for analyzing local Hardy spaces with weights

Abstract

In this paper, we give a characterization of weighted local Hardy spaces $h^1_\wz(\rz)$ associated with local weights by using the truncated Reisz transforms, which generalizes the corresponding result of Bui in \cite{b}.