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Generalized fractional integral operators and their commutators with functions in generalized Campanato spaces on Orlicz spaces. (English) Zbl 07142977
Summary: We investigate the commutators \([b,I_{\rho}]\) of generalized fractional integral operators \(I_{\rho}\) with functions \(b\) in generalized Campanato spaces and give a necessary and sufficient condition for the boundedness of the commutators on Orlicz spaces. To do this we define Orlicz spaces with generalized Young functions and prove the boundedness of generalized fractional maximal operators on the Orlicz spaces.

MSC:
47 Operator theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B35 Function spaces arising in harmonic analysis
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