Weak type estimates for intrinsic square functions on the weighted Morrey spaces

TL;DR

This paper establishes weak type estimates for intrinsic square functions such as the Lusin area integral and Littlewood-Paley functions on weighted Morrey spaces, expanding understanding of their boundedness properties.

Contribution

It provides new weak type estimates for intrinsic square functions on weighted Morrey spaces, a novel extension in harmonic analysis.

Findings

Weak type estimates for intrinsic square functions on weighted Morrey spaces.

Extension of boundedness results to the case $0<<1$ with $w\u2208 A_1$.

Enhanced understanding of harmonic analysis operators on weighted Morrey spaces.

Abstract

In this paper, we will obtain the weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{1,\kappa}(w)$ for $0<\kappa<1$ and $w\in A_1$.