Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T11:26:22.739Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)