One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in $\\R^n$. When the support is a smooth enough manifold, an almost complete picture is available. One of the early results in this direction is the following: Let $f\\in C_c^{\\infty}(d\\sigma)$, where $d\\sigma$ is the surface measure on the sphere $S^{n-1}\\subset\\R^n$. Then

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