Weighted local Hardy spaces and their applications

TL;DR

This paper investigates weighted local Hardy spaces associated with local weights, including classical Muckenhoupt weights, extending existing theories of local and weighted Hardy spaces.

Contribution

It introduces a unified framework for weighted local Hardy spaces that encompasses classical and weighted Hardy space theories.

Findings

Established properties of weighted local Hardy spaces

Extended classical Hardy space theory to weighted settings

Included Muckenhoupt weights in the local Hardy space framework

Abstract

In this paper, we study weighted local Hardy spaces $h^p_\wz(\rz)$ associated with local weights which include the classical Muckenhoupt weights. This setting includes the classical local Hardy space theory of Goldberg \cite{g}, and the weighted Hardy spaces of Bui \cite{bu}.