Cargando…
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 [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 a...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5391400/ https://www.ncbi.nlm.nih.gov/pubmed/28469352 http://dx.doi.org/10.1186/s13660-017-1349-4 |
Sumario: | 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. |
---|