Equivalence of $K$-functionals and modulus of smoothness for Fourier transform


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


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.


  • Receive Date: 03 September 2011
  • Revise Date: 03 September 2012
  • Accept Date: 03 September 2012
  • First Publish Date: 03 September 2012