An Lp Fourier analysis on symmetric spaces

AbstractSpherical Fourier transforms of Lp (1 ⩽ p < 2) functions on a Riemannian symmetric space are studied. It is proved that the spherical transform of such a function extends holomorphically to the same domain of the dual space as the one where the spherical transform of a Schwartz function of Lp type extends holomorphically and is rapidly decreasing (cf. [11]). And also, it is proved that a Hausdorff-Young inequality and a Riemann-Lebesgue lemma hold in the domain