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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 4, 2007, pp. 377–390
DOI: 10.4171/ZAA/1330

Published online: 2007-12-31

Nontangential Limits of Poisson Integrals Associated to Dunkl Operators for Dihedral Groups

Florence Scalas[1]

(1) Université de Provence, Marseille, France

In this paper we study the differentiation and maximal functions of complex Borel measures on the unit circle of $\C$ with respect to the measures associated to Dunkl differential-difference operators for dihedral groups. We prove that the Poisson integrals corresponding to these differential-difference operators have nontangential limits almost everywhere. Our approach relies on the proof of the doubling condition to obtain an appropriate covering lemma.

Keywords: Dunkl operators, covering lemma, maximal function, Poisson integrals, nontangential limits

Scalas Florence: Nontangential Limits of Poisson Integrals Associated to Dunkl Operators for Dihedral Groups. Z. Anal. Anwend. 26 (2007), 377-390. doi: 10.4171/ZAA/1330