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

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