### 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.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Ren, Jiagang; Röckner, MichaelUniBi
Einrichtung
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.
Stichworte
Holder-continuity; quantum fields; Sobolev spaces in infinite dimensions; Euclidean; fractional order; irreducibility; Dirichlet forms; Malliavin calculus
Erscheinungsjahr
2000
Zeitschriftentitel
Probability Theory and Related Fields
Band
117
Ausgabe
2
Seite(n)
201-220
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/1619467

### Zitieren

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. https://doi.org/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.

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