GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE DUNKL TRANSFORM IN THE SPACE L^P(R)

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the(\psi,p)-Lipschitz Dunkl condition in the space \mathrm{L}_{p,\alpha}=\mathrm{L}^{p}(\mathbb{R},|x|^{۲\alpha+۱}dx)‎, ‎where \alpha>-\frac{۱}{۲}.

Keywords:

Dunkl operator , Dunkl transform , generalized translation Dunkl operator