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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2023 Volume 323, Pages 65–86 (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

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.

UDC: 517.51

Received: May 7, 2023
Revised: August 2, 2023
Accepted: August 9, 2023

DOI: 10.4213/tm4354


 English version: Proceedings of the Steklov Institute of Mathematics, 2023, 323, 59–80

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© Steklov Math. Inst. of RAS, 2025