using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; 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.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

This article describes a class of pseudo-differential operators(A??)(x)=F??x?1([max?{|?1(||?||p)|,|?2(||?||p)|}]???ˆ(?)), ??D(Qpn) and ??C; here [max?{|?1(||?||p)|,|?2(||?||p)|}]?? is the symbol operator A?. These operators can be seen as generalization Bessel potentials in p-adic context. We show that family (K?)?>0 convolution kernels attached to generalized A?, ?>0, determine semigroup on Qp...