Smoothness and Function Spaces Generated by Homogeneous Multipliers

Abstract EN

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.