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The inversion formula for the spherical Fourier transform on a noncompact symmetric space is shown to hold a.e. for      L p ( G / K ) , 1 ⩽  p &gt; 2 {L^p}(G/K),1 \leqslant p &gt; 2      .

Pointwise inversion of the spherical transform on 𝐿^{𝑝}(𝐺/𝐾), 1≤𝑝<2