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Boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces. (English) Zbl 1311.42049
Summary: We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $$M^{\Phi,\phi}_{w}({\mathbb{R}}^n)$$. 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.

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35 Function spaces arising in harmonic analysis 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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