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

TL;DR

This paper presents new Lusin-type approximation results for Sobolev functions with specific integrability conditions on Gaussian spaces, using novel pointwise estimates based on semigroup techniques.

Contribution

It introduces new approximation results for Sobolev functions on infinite-dimensional Gaussian spaces, utilizing innovative pointwise estimates and semigroup methods.

Findings

Established Lusin-type approximation results for Sobolev functions

Developed new pointwise estimates for function approximations

Applied semigroup techniques to infinite-dimensional Gaussian spaces

Abstract

We establish new approximation results in the sense of Lusin for Sobolev functions $f$ with $|\nabla f| \in L\log L$ on infinite-dimensional spaces equipped with Gaussian measures. The proof relies on some new pointwise estimate for the approximations based on the corresponding semigroup which can be of independent interest.