Some estimates of intrinsic square functions on weighted Herz-type Hardy spaces

TL;DR

This paper establishes strong and weak type estimates for intrinsic square functions on weighted Herz-type Hardy spaces using atomic decomposition techniques.

Contribution

It introduces new estimates for intrinsic square functions on weighted Herz-type Hardy spaces, expanding the understanding of their boundedness properties.

Findings

Strong type estimates for Lusin area function.

Weak type estimates for Littlewood-Paley $ ext{G}$-function.

Boundedness results for $ ext{G}^*_ ext{lambda}$-function.

Abstract

In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $\mathcal G$-function and $\mathcal G^*_\lambda$-function on these spaces.