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 $r$.