Boundedness of intrinsic square functions on generalized Morrey spaces

TL;DR

This paper investigates the boundedness of intrinsic square functions and their commutators on generalized Morrey spaces, providing strong and weak type estimates under certain growth conditions.

Contribution

It establishes boundedness results for intrinsic square functions and their commutators on generalized Morrey spaces, extending previous work to broader function spaces.

Findings

Boundedness of intrinsic square functions on generalized Morrey spaces.

Weak and strong type estimates are proved under doubling conditions.

Boundedness of commutators with BMO functions is demonstrated.

Abstract

In this paper, we will study 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 generalized Morrey spaces $L^{p,\Phi}$ for $1\le p<\infty$, where $\Phi$ is a growth function on $(0,\infty)$ satisfying the doubling condition. The boundedness of the commutators generated by $BMO(\mathbb R^n)$ functions and intrinsic square functions is also obtained.