Intrinsic square functions on functions spaces including weighted Morrey spaces

TL;DR

This paper establishes the boundedness of intrinsic square functions, such as Lusin area integral and Littlewood-Paley $g^{ ext{*}}_{ ext{lambda}}$, on weighted Morrey spaces and related function spaces, including commutators.

Contribution

It extends the boundedness results of intrinsic square functions to weighted Morrey spaces and analyzes the behavior of associated commutators generated by BMO functions.

Findings

Intrinsic square functions are bounded on weighted Morrey spaces.

Commutators with BMO functions are also bounded in these spaces.

Results generalize previous boundedness theorems to broader function spaces.

Abstract

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.