A note on Lusin-type approximation of Sobolev functions on Gaussian\n spaces

2019/08/27 by А. N. Shaposhnikov, Shaposhnikov, Alexander
Mathematics · #28C20 #46E35 #60H07 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1908.10183

openalex publication_date 2019/08/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We establish new approximation results in the sense of Lusin for Sobolev\nfunctions f with |\∇ f| \∈ L\log L on infinite-dimensional spaces\nequipped with Gaussian measures. The proof relies on some new pointwise\nestimate for the approximations based on the corresponding semigroup which can\nbe of independent interest.\n

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