The Riesz Potential Operator in Optimal Couples of Rearrangement Invariant Spaces

Claudia Capone; Alberto Fiorenza; G. E. Karadzhov; Waqas Nazeer

doi:10.4171/zaa/1432

JournalszaaVol. 30, No. 2pp. 219–236

The Riesz Potential Operator in Optimal Couples of Rearrangement Invariant Spaces

Claudia Capone
Consiglio Nazionale delle Ricerche, Napoli, Italy
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Alberto Fiorenza
Università degli Studi di Napoli Federico II, Italy
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G. E. Karadzhov
Bulgarian Acedemy of Sciences, Sofia, Bulgaria
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Waqas Nazeer
GC University, Lahore, Pakistan
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- zbMATH Open

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Abstract

We prove continuity of the Riesz potential operator in optimal couples of rearrangement invariant function spaces defined in $R^{n}$ with the Lebesgue measure. An application is given to the Hardy–Littlewood maximal operator.

Cite this article

Claudia Capone, Alberto Fiorenza, G. E. Karadzhov, Waqas Nazeer, The Riesz Potential Operator in Optimal Couples of Rearrangement Invariant Spaces. Z. Anal. Anwend. 30 (2011), no. 2, pp. 219–236

DOI 10.4171/ZAA/1432