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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 323, Pages 65–86
DOI: https://doi.org/10.4213/tm4354 (Mi tm4354) 		 
Sobolev and Besov Classes on Infinite-Dimensional Spaces

V. I. Bogachevab

a Lomonosov Moscow State University, Moscow, 119991 Russia
b National Research University Higher School of Economics, Pokrovskii bul. 11, Moscow, 109028 Russia
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DOI: https://doi.org/10.4213/tm4354
Abstract: We discuss various definitions of Sobolev and Besov classes on infinite-dimensional spaces, give a survey of the results on coincidence of some of these classes, and obtain a number of new results.
Keywords: Sobolev space, Besov space, Gaussian measure, differentiable measure.
Funding agency Grant number
Russian Science Foundation 22-11-00015
This work was supported by the Russian Science Foundation under grant no. 22-11-00015, https://rscf.ru/en/project/22-11-00015/, and performed at Lomonosov Moscow State University.
Received: May 7, 2023
Revised: August 2, 2023
Accepted: August 9, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 323, Pages 59–80
DOI: https://doi.org/10.1134/S0081543823050048
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: V. I. Bogachev, “Sobolev and Besov Classes on Infinite-Dimensional Spaces”, Theory of Functions of Several Real Variables and Its Applications, Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday, Trudy Mat. Inst. Steklova, 323, Steklov Mathematical Institute of RAS, Moscow, 2023, 65–86; Proc. Steklov Inst. Math., 323 (2023), 59–80
Citation in format AMSBIB
\Bibitem{Bog23}
\by V.~I.~Bogachev
\paper Sobolev and Besov Classes on Infinite-Dimensional Spaces
\inbook Theory of Functions of Several Real Variables and Its Applications
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 323
\pages 65--86
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4354}
\crossref{https://doi.org/10.4213/tm4354}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4716515}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 323
\pages 59--80
\crossref{https://doi.org/10.1134/S0081543823050048}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85186879927}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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