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

• 成果类型: Article
• 署名作者: Ren, JG; Röckner, M
• 署名单位: Huazhong University of Science & Technology; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050004
• 发表日期: 2000
• 页码: 201-220
• 关键词: planar brownian-motion; wiener space; FORMULA; STATES

摘要

We prove Holder-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.