New estimates for the Fourier transform in the space L2(Rn)

Abstract

In this paper, we prove new estimates are presented for the integral \int_{|t|>N}|\widehat(f)(t)|^{2}dt , where \widehat(f) stands for the Fourier transform of f and N ≥ 1, in the space L2(Rn) characterized by the generalized modulus of continuity of the kth order constructed with the help of the generalized spherical mean operator.