JournalszaaVol. 24 , No. 1DOI 10.4171/zaa/1228

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

  • Niels Jacob

    University of Wales, Swansea, UK
  • René L. Schilling

    Technische Universität Dresden, Germany
Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel) cover

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.