Document Type : Research Paper

Authors

• R. Daher
• M. El Hamma

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

Abstract

In Hilbert space $L^2(\mathbb{R}^n)$, we prove the equivalence between the modulus of smoothness and the $K$-functionals constructed by the Sobolev space corresponding to the Fourier transform. For this purpose, using a spherical mean operator.

Keywords

• Fourier Transform
• spherical mean operator
• K-functionals
• modulus of smoothness