Dunkl Translation and Uncentered Maximal Operator on the Real Line

Chokri Abdelkefi and Mohamed Sifi

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-9

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 L p -boundedness of this operator for 1 < p ≤ + ∞ .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:087808

DOI: 10.1155/2007/87808

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