JournalszaaVol. 24, No. 1pp. 3–28

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
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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.

Cite this article

Niels Jacob, René L. Schilling, Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel). Z. Anal. Anwend. 24 (2005), no. 1, pp. 3–28

DOI 10.4171/ZAA/1228