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REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

Published online by Cambridge University Press:  09 June 2003

JUHA KINNUNEN  and
EERO SAKSMAN
JUHA KINNUNEN
Affiliation:
Department of Mathematics and Statistics, P.O. Box 35 (MaD), FIN-40014 University of Jyväskylä, Finlandsaksman@maths.jyu.fi
EERO SAKSMAN
Affiliation:
Institute of Mathematics, P.O. Box 1100, FIN-02015 Helsinki University of Technology, Finlandjuha.kinnunen@hut.fi
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Abstract

The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps $L^p$-spaces boundedly into certain first-order Sobolev spaces. It is also proved that the fractional maximal operator preserves first-order Sobolev spaces. This extends known results for the Hardy–Littlewood maximal operator.

Keywords

42B2546E35
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 4 , July 2003 , pp. 529 - 535
Copyright
© The London Mathematical Society 2003

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