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Zeitschrift für Analysis und ihre Anwendungen


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Volume 30, Issue 2, 2011, pp. 219–236
DOI: 10.4171/ZAA/1432

Published online: 2011-04-03

The Riesz Potential Operator in Optimal Couples of Rearrangement Invariant Spaces

Claudia Capone[1], Alberto Fiorenza[2], G. E. Karadzhov[3] and Waqas Nazeer[4]

(1) Consiglio Nazionale delle Ricerche, Napoli, Italy
(2) Università degli Studi di Napoli Federico II, Italy
(3) Bulgarian Acedemy of Sciences, Sofia, Bulgaria
(4) GC University, Lahore, Pakistan

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

Keywords: Riesz potential operator, rearrangement invariant function spaces, real interpolation

Capone Claudia, Fiorenza Alberto, Karadzhov G. E., Nazeer Waqas: The Riesz Potential Operator in Optimal Couples of Rearrangement Invariant Spaces. Z. Anal. Anwend. 30 (2011), 219-236. doi: 10.4171/ZAA/1432