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We derive bilateral estimates for the constants appearing in the Fouriertransform restricted theorems on the Euclidean sphere for the ordinary andespecially radial functions belonging to the Lebesgue-Riesz spaces as well asbelonging to the Grand Lebesgue Spaces.  We obtain an exact estimate for the norm of the restriction Fourier transformoperator acting on the radial functions.

Sharp bounds for the spherical restriction Fourier transform in classical Lebesgue-Riesz and Grand Lebesgue spaces for ordinary and radial functions