Weak type estimates of intrinsic square functions on the weighted Hardy spaces

TL;DR

This paper establishes weighted weak type estimates for intrinsic square functions such as the Lusin area function and Littlewood-Paley functions on weighted Hardy spaces, using atomic decomposition techniques.

Contribution

It provides new weighted weak type bounds for intrinsic square functions on weighted Hardy spaces, expanding the understanding of their behavior in these settings.

Findings

Weighted weak type estimates for intrinsic square functions are proved.

Atomic decomposition is used to derive these estimates.

Results apply to Lusin area, g, and g* functions.

Abstract

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