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

Ren J, Röckner M (2000)
Probability Theory and Related Fields 117(2): 201-220.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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 alpha is an element of (1/p, 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.
Erscheinungsjahr
Zeitschriftentitel
Probability Theory and Related Fields
Band
117
Ausgabe
2
Seite(n)
201-220
ISSN
PUB-ID

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Ren J, Röckner M. Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probability Theory and Related Fields. 2000;117(2):201-220.
Ren, J., & Röckner, M. (2000). Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probability Theory and Related Fields, 117(2), 201-220. doi:10.1007/s004400050004
Ren, J., and Röckner, M. (2000). Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probability Theory and Related Fields 117, 201-220.
Ren, J., & Röckner, M., 2000. Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probability Theory and Related Fields, 117(2), p 201-220.
J. Ren and M. Röckner, “Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications”, Probability Theory and Related Fields, vol. 117, 2000, pp. 201-220.
Ren, J., Röckner, M.: Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications. Probability Theory and Related Fields. 117, 201-220 (2000).
Ren, Jiagang, and Röckner, Michael. “Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications”. Probability Theory and Related Fields 117.2 (2000): 201-220.