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Comptes Rendus Mathématique
Volume 338, n° 1
pages 31-34 (janvier 2004)
Doi : 10.1016/j.crma.2003.11.005
Received : 15 August 2003 ;  accepted : 7 November 2003
La fonction maximale de Hardy-Littlewood sur une classe d'espaces métriques mesurables
The Hardy-Littlewood maximal function on some metric measure spaces

Hong-Quan  Li
Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Allemagne 

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Dans cette Note, on se propose d'étudier le comportement de la fonction maximale de Hardy-Littlewood,  , sur l'espace cuspidale en termes de la croissance du volume de la base. En particulier, on montre que pour tout   fixé, il existe une variété sur laquelle l'opérateur   est borné sur   pour   mais pas pour  . Pour citer cet article : H.-Q. Li, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Abstract

In this Note, we study the behavior of the Hardy-Littlewood maximal function   on cusp manifolds in terms of the growth of the volume of the base space. In particular, we prove that for all   fixed, there exists such a manifold on which   is bounded on   for   but not for  . To cite this article: H.-Q. Li, C. R. Acad. Sci. Paris, Ser. I 338 (2004).




© 2003  Académie des sciences@@#104156@@

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