Generalization of Dunkl Dini Lipschitz Functions

Salah El Ouadih, Radouan Daher

Abstract

Using a generalized spherical mean operator, we obtain a generalization of Younis’s Theorem 5.2 in [12] for the Dunkl transform for functions satisfying the d-Dunkl Dini Lipschitz condition in the space Lp(Rd,wl(x)dx), 1 < p ≤ 2, where wl is a weight function invariant under the action of an associated reflection group. 

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