2021/07/20 by Yifei Zheng, Zheng, Yifei, Zachary Selk +1
Mathematics · #28C20 #46G12 #60B11 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2107.09440
openalex publication_date 2021/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fréchet space X over \mathbb R admits some full measure Banach intermediate space between X and its Cameron-Martin space. We provide a way of generating such spaces and, by showing a partial converse, give a characterization of Banach intermediate spaces. Finally, we show an example of constructing an α-Hölder intermediate space in the space of continuous functions, \mathcal C0[0, 1] with the classical Wiener measure.