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arXiv · 1908.10183

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

Alexander Shaposhnikov
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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.

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Alexander Shaposhnikov. 2020-12-09. A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. https://arxiv.org/abs/1908.10183

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