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

Shaposhnikov A (2021)
Journal of Functional Analysis 280(6): 108917.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We establish new approximation results in the sense of Lusin for Sobolev functions f with vertical bar del f vertical bar is an element of 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. (c) 2020 Elsevier Inc. All rights reserved.
Stichworte
Sobolev class; Gaussian measure; Ornstein-Uhlenbeck semigroup; Lusin-type approximation
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Functional Analysis
Band
280
Ausgabe
6
Art.-Nr.
108917
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2951292

Zitieren

Shaposhnikov A. A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. Journal of Functional Analysis. 2021;280(6): 108917.
Shaposhnikov, A. (2021). A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. Journal of Functional Analysis, 280(6), 108917. https://doi.org/10.1016/j.jfa.2020.108917
Shaposhnikov, A. (2021). A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. Journal of Functional Analysis 280:108917.
Shaposhnikov, A., 2021. A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. Journal of Functional Analysis, 280(6): 108917.
A. Shaposhnikov, “A note on Lusin-type approximation of Sobolev functions on Gaussian spaces”, Journal of Functional Analysis, vol. 280, 2021, : 108917.
Shaposhnikov, A.: A note on Lusin-type approximation of Sobolev functions on Gaussian spaces. Journal of Functional Analysis. 280, : 108917 (2021).
Shaposhnikov, Alexander. “A note on Lusin-type approximation of Sobolev functions on Gaussian spaces”. Journal of Functional Analysis 280.6 (2021): 108917.

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