Generalization of Titchmarsh's Theorem for the Dunkl Transform

Document Type : Full Length Article


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Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's
theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition
in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the
action of an associated re
ection group.