In this paper, we prove a genuine analogue of the Wiener Tauberian theorem for {L^{p,1}(G)} ({1\leq p<2}), with {G=\mathrm{SL}(2,\mathbb{R})}.

We prove a genuine analogue of Wiener Tauberian theorem for integrable functions on SL(2, R).

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The aim of this paper is to study L p -boundedness property of the pseudo differential operator associated with a symbol, on rank one Riemannian symmetric spaces of noncompact type, where the symbol satisfies Hörmander-type conditions near infinity.