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

摘要

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