EXTENSIONS OF H-LIPSCHITZIAN MAPPINGS WITH INFINITE-DIMENSIONAL RANGE

Abstract

Let γ be a Radon Gaussian measure on a locally convex space X with the Cameron–Martin space H, let A⊂X be a γ-measurable set, and let F: A→ E be a γ-measurable mapping with values in a separable Hilbert space E such that |F(x)-F(y)|E ≤C|x-y|H whenever x, y∈A, x-y∈H. The main result in this work gives a γ-measurable extension of F to all of X such that |F(x+h)-F(x)|E≤C|h|H for all x∈X and h∈H. Some related results are obtained.