On some spaces of functions of fractional (complex) smoothness

摘要

We give a characterization of functions of fractional (complex order) smoothness on terms of L_p_1,--,p_n (anisotropic) Lizorkin type mixed norm convergent convolutions with kernels expressed by means of elementary functions. These spaces of L_p-functions have been introduced by P.I. Lizorkin as spaces which have generalized Liouville derivatives. They have also been considered by S. Samko in the isotropic case and by A. Davtyan and V. Nogin in the anisotropic case. We also consider the anisotropic complex order case and give a simple description of the involved spaces.