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A note on Lusin-type approximation of Sobolev functions on Gaussian spaces
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jfa.2020.108917
Alexander Shaposhnikov

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.

中文翻译:

关于高斯空间上 Sobolev 函数的 Lusin 型逼近的注记

我们将 $L^1$ 中的 Shigekawa 的 Meyer 型不等式扩展到更一般的 Ornstein-Uhlenbeck 算子,并在 Lusin 意义上为 Sobolev 函数 $f$ 和 $|\nabla f| 建立新的近似结果 \in L\log L$ 在配备高斯测度的无限维空间上。该证明依赖于基于相应半群的近似值的一些新的逐点估计,这些半群可以是独立感兴趣的。
更新日期:2021-03-01
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