Boundedness of intrinsic square functions on the weighted weak Hardy spaces

TL;DR

This paper proves the boundedness of intrinsic square functions such as the Lusin area integral and Littlewood-Paley functions on weighted weak Hardy spaces using atomic decomposition techniques.

Contribution

It establishes new boundedness results for intrinsic square functions on weighted weak Hardy spaces, expanding understanding of their behavior in these function spaces.

Findings

Boundedness of Lusin area integral on weighted weak Hardy spaces

Boundedness of Littlewood-Paley g-function on these spaces

Boundedness of g*_unction on these spaces

Abstract

In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on these spaces.