Equivalence of K-functional and modulus of smoothness constructed by Fourier-Bessel transform in the space L2,γ(ℝn+)

Abstract

Using a generalized shift operator, we define generalized modulus of smothness in the space L_2,γ(ℝ_n⁺). Based on the Laplace-Bessel differential operator we define Sobolev-type space and K-functionals. In this paper paper we prove the equivalence theorem for a K-functional and a modulus of smoothness for the Fourier-Bessel transformation on ℝ_n⁺.