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Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications
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  • Published: June 2000

Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications

  • Jiagang Ren1 &
  • Michael Röckner2 

Probability Theory and Related Fields volume 117, pages 201–220 (2000)Cite this article

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  • 5 Citations

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Abstract.

We prove Hölder-continuity on rays in the direction of vectors in the (generalized) Cameron-Martin space for functions in Sobolev spaces in L p of fractional order α∈ (, 1) over infinite dimensional linear spaces. The underlying measures are required to satisfy some easy standard structural assumptions only. Apart from Wiener measure they include Gibbs measures on a lattice and Euclidean interacting quantum fields in infinite volume. A number of applications, e.g., to the two-dimensional polymer measure, are presented. In particular, irreducibility of the Dirichlet form associated with the latter measure is proved without restrictions on the coupling constant.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China, , , , , , CN

    Jiagang Ren

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätstr.25, 33615 Bielefeld, Germany. e-mail: roeckner@mathematik.uni-bielefeld.de, , , , , , DE

    Michael Röckner

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  1. Jiagang Ren
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  2. Michael Röckner
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Received: 9 November 1998 / Published online: 30 March 2000

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Ren, J., Röckner, M. Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probab Theory Relat Fields 117, 201–220 (2000). https://doi.org/10.1007/s004400050004

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  • Issue Date: June 2000

  • DOI: https://doi.org/10.1007/s004400050004

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Keywords

  • Sobolev Space
  • Infinite Dimension
  • Fractional Sobolev Space
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