Regularity of the Fractional Maximal Function |
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| Authors: | Kinnunen Juha; Saksman Eero |
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| Institution: | Institute of Mathematics P.O. Box 1100, FIN-02015 Helsinki University of Technology, Finland; juha.kinnunen{at}hut.fi
Department of Mathematics and Statistics P.O. Box 35 (MaD), FIN-40014 University of Jyväskylä, Finland; saksman{at}maths.jyu.fi |
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| Abstract: | The purpose of this work is to show that the fractional maximaloperator has somewhat unexpected regularity properties. Themain result shows that the fractional maximal operator mapsLp-spaces boundedly into certain first-order Sobolev spaces.It is also proved that the fractional maximal operator preservesfirst-order Sobolev spaces. This extends known results for theHardy-Littlewood maximal operator. 2000 Mathematics SubjectClassification 42B25, 46E35. |
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