The boundedness of intrinsic square functions on the weighted Herz spaces

TL;DR

This paper establishes strong and weak type estimates for intrinsic square functions, such as the Lusin area integral and Littlewood-Paley functions, on weighted Herz spaces with general weights, advancing harmonic analysis understanding.

Contribution

It provides new boundedness results for intrinsic square functions on weighted Herz spaces, extending previous work to more general weights and function spaces.

Findings

Strong and weak type estimates obtained

Boundedness of intrinsic square functions established

Results applicable to general weights in Herz spaces

Abstract

In this paper, we will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Herz spaces $\dot K^{\alpha,p}_q(w_1,w_2)$ ($K^{\alpha,p}_q(w_1,w_2)$) with general weights.