Boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces

TL;DR

This paper studies the boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces, providing conditions based on Zygmund-type inequalities without requiring monotonicity of the space parameters.

Contribution

It establishes new boundedness criteria for intrinsic square functions and their commutators on these complex function spaces, expanding understanding without monotonicity assumptions.

Findings

Boundedness conditions expressed via Zygmund-type inequalities

No monotonicity assumption needed for the weight functions

Applicable to a broad class of weighted Orlicz-Morrey spaces

Abstract

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on weights $\varphi$ without assuming any monotonicity property of $\varphi(x,\cdot)$ with $x$ fixed.