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

Alexander Shaposhnikov

Published 2019-08-27Version 1

We extend Shigekawa's Meyer-type inequality in $L^1$ to more general Ornstein-Uhlenbeck operators and 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.