Equivalence of K-functionals and modulus of smoothness for fourier transform

Authors

Department of Mathematics, Faculty of Science An Chock, University Hassan II, Casablanca, Morocco

Abstract

In Hilbert space L2(Rn), we prove the equivalence between the mod-
ulus of smoothness and the K-functionals constructed by the Sobolev space cor-
responding to the Fourier transform. For this purpose, Using a spherical mean
operator.

Keywords