Smoothness and Function Spaces Generated by Homogeneous Multipliers - Konstantin Runovski; Hans-Jürgen Schmeisser (Journal of Function Spaces and Applications)
Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for ψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.