Boundedness of Intrinsic Square Functions and their Commutators on Generalized Orlicz-Morrey Spaces

Abstract

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