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Riesz potential and its commutators on Orlicz spaces
Vagif S Guliyev1,2, Fatih Deringoz1, Sabir G Hasanov3
1Department of Mathematics, Ahi Evran University, Kirsehir, Turkey.
Abstract:
In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator [Formula: see text] on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1):247-286, 2011) found necessary and sufficient conditions on general Young functions Φ and Ψ ensuring that this operator is of weak or strong type from [Formula: see text] into [Formula: see text]. Our characterizations for the boundedness of the above-mentioned operator are different from the ones in (Cianchi in J. Lond. Math. Soc. 60(1):247-286, 2011). As an application of these results, we consider the boundedness of the commutators of Riesz potential operator [Formula: see text] on Orlicz spaces when b belongs to the BMO and Lipschitz spaces, respectively.
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