Fractional integrals of periodic functions of several variables

Abstract

In this paper it has been systematically studied the imbedding properties of fractional integral operators of periodic functions of several variables, and isomorphic properties of fractional integral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration, the space of Lipschitz continuous functions and the Sobolev space are identical in L2-norm. Results obtained here are not true for fractional integrals (or Riesz potentials) in ℝ n .