Equivalence of K-functionals and modulus of smoothness generated by the (k,n)-Fourier transform
Mehrez Mannai, Selma Negzaoui, Sami Rebhi · Asian-European Journal of Mathematics · 2025
By considering a generalized translation operator related to the [Formula: see text]-Fourier transform, we define the corresponding modulus of smoothness and [Formula: see text]-functionals. We prove their equivalence in [Formula: see text], extending classical results to this generalized harmonic analysis framework. This lays the groundwork for future applications to the study of function spaces such as Lipschitz and Besov-type spaces.