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In this paper, we prove a genuine analogue of the Wiener Tauberian theorem forL   p  ,  1    ⁢   (  G  ){L^{p,1}(G)}    (1  ≤  p  &lt;  2{1\leq p&lt;2}   ), withG  =   SL  ⁢   (  2  ,  ℝ  ){G=\mathrm{SL}(2,\mathbb{R})}   .

A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on SL(2,ℝ)