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.
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Florence Scalas, Nontangential Limits of Poisson Integrals Associated to Dunkl Operators for Dihedral Groups. Z. Anal. Anwend. 26 (2007), no. 4, pp. 377–390DOI 10.4171/ZAA/1330