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.) |
Keywords:
intrinsic square functions; commutators; generalized weighted Orlicz-Morrey spaces; Zygmund-type integral inequalities; BMO functionsReferences:
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