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

Abstract: We derive bilateral estimates for the constants appearing in the Fourier transform restricted theorems on the Euclidean sphere for the ordinary and especially radial functions belonging to the Lebesgue-Riesz spaces as well as belonging to the Grand Lebesgue Spaces. We obtain an exact estimate for the norm of the restriction Fourier transform operator acting on the radial functions.