International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 87808, 9 pages
doi:10.1155/2007/87808
Research Article

Dunkl Translation and Uncentered Maximal Operator on the Real Line

Chokri Abdelkefi1 and Mohamed Sifi2

1Department of Mathematics, Preparatory Institute for Engineering Studies of Tunis, Monfleury, Tunis 1089, Tunisia
2Department of Mathematics, Faculty of Sciences of Tunis, Tunis-El Manar University, Tunis 1060, Tunisia

Received 22 November 2006; Accepted 5 July 2007

Academic Editor: Ahmed Zayed

Copyright © 2007 Chokri Abdelkefi and Mohamed Sifi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish estimates of the Dunkl translation of the characteristic function χ[−ɛ,ɛ], ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type (1,1). As a consequence, we obtain the Lp-boundedness of this operator for 1<p≤+∞.