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