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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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