Ray Holder-continuity for fractional Sobolev spaces in infinite dimensionsand applications

We prove Holder-continuity on rays in the direction of vectors in the (gene ralized) Cameron-Martin space for functions in Sobolev spaces in L-p Of fra ctional order alpha is an element of (1/p, 1) over infinite dimensional lin ear spaces. The underlying measures are required to satisfy some easy stand ard structural assumptions only. Apart from Wiener measure they include Gib bs measures on a lattice and Euclidean interacting quantum fields in infini te volume. A number of applications, e.g., to the two-dimensional polymer m easure, are presented. In particular, irreducibility of the Dirichlet form associated with the latter measure is proved without restrictions on the co upling constant.