Dunkl translation and uncentered maximal operator on the real line
type: Item
instance of: scholarly article
title: Dunkl translation and uncentered maximal operator on the real line
zbMATH Open document ID: 1201.42012
DOI: 10.1155/2007/87808
author: Chokri Abdelkefi
author: Mohamed Sifi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/45187
review text: Summary: We establish estimates of the Dunkl translation of the characteristic function \(\chi _{[ - \varepsilon ,\varepsilon]}, \varepsilon >0\), 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 \(L^p\)-boundedness of this operator for \(1<p\leq +\infty \). Remark: Note that for the centered maximal function associated to any finite reflection group on \(\mathbb R^n\) the same result has been proved by \textit{S. Thangavelu} and \textit{Y. Xu} [J. Anal. Math. 97, 25--55 (2006; Zbl 1131.43006)].
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 5282512
MaRDI profile type: Publication
OpenAlex ID: W2060833120
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description: scientific article; zbMATH DE number 5282512