On the Schwartz space isomorphism theorem for rank one symmetric space
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- Jana, J. & Sarkar, R.P. Proc Math Sci (2007) 117: 333. doi:10.1007/s12044-007-0029-6
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In this paper we give a simpler proof of the Lp-Schwartz space isomorphism (0 < p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker’s  proof of the corresponding result in the case of left K-invariant functions on X. Thus we give a proof which relies only on the Paley-Wiener theorem.