Riesz potential and its commutators on Orlicz spaces

In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator I α 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 t...

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Bibliographic Details
Published in:Journal of inequalities and applications 2017-04, Vol.2017 (1), p.1-18, Article 75
Main Authors: Guliyev, Vagif S, Deringoz, Fatih, Hasanov, Sabir G
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
BMO
commutator
Commutators
Inequalities
Lipschitz space
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Orlicz space
Proceedings of the International Conference on Analysis and Applications
Riesz potential
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Summary:In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator I α 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 L Φ into L Ψ . 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 [ b , I α ] on Orlicz spaces when b belongs to the BMO and Lipschitz spaces, respectively.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-017-1349-4