Let G/K be a compact symmetric space of rank one. The aim of this paper is to give sufficient conditions for the Cv -smoothness of the Radon Nikodym derivative fa1,...,ap = d (μa1 * ... * μap of the convolution μa1 *...*μap of some orbital measures μai, with respect to the Haar measure μG of G. This generalizes some of the main results in , in the case of compact rank one symmetric spaces, where the absolute continuity of the measure μa1 * ... * μap with respect to dμG was considered. Our main result generalizes also the main results in  and , where the L2-regularity was considered. As a consequence of our main result, we give sufficient conditions for fa1,...,ap to be in Lq (G, dμG) for all q ge; 1 and for the Fourier series of fa1,...,ap to converge absolutely and uniformly to fa1,...,ap.
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