Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel)

Abstract

V. G. Maz'ya and J. Nagel [Beitr. Anal. 12 (1978) 7–17] found for certain classes of weighted Sobolev norms (defined using the Fourier transform) equivalent Slobodeckij-type difference representations. We extend these considerations to a wider class of anisotropic norms which arise in the theory of Markov processes. In particular we show that these Sobolev norms are equivalent to Dirichlet norms.