The intrinsic square function characterizations of weighted Hardy spaces

TL;DR

This paper investigates the boundedness and characterizations of intrinsic square functions on weighted Hardy spaces $H^p(w)$ for $0<p<1$, providing new insights into their structure and properties.

Contribution

It introduces intrinsic square function characterizations of weighted Hardy spaces $H^p(w)$ for $0<p<1$, extending existing theory.

Findings

Boundedness of intrinsic square functions on $H^p(w)$ for $0<p<1$

New intrinsic square function characterizations of weighted Hardy spaces

Enhanced understanding of the structure of weighted Hardy spaces

Abstract

In this paper, we will study the boundedness of intrinsic square functions on the weighted Hardy spaces $H^p(w)$ for $0<p<1$, where $w$ is a Muckenhoupt's weight function. We will also give some intrinsic square function characterizations of weighted Hardy spaces $H^p(w)$ for $0<p<1$.