Sobolev classes of functions of generalized differentiability belong to the major analytic achievements in the XX century and have found impressive applications in the most diverse areas of mathematics. So it does not come as a surprise that their infinite-dimensional analogs attract considerable attention. It was already at the end of the 60s and the beginning of the 70s of the last century that in the works of N. N. Frolov, Yu. L. Daletskiĭ, L. Gross, M. Krée, and P. Malliavin Sobolev classes with respect to Gaussian measures on infinite-dimensional spaces were introduced and studied. Their first triumph came with the development of the Malliavin calculus since the mid of the 70s. At present, such classes and their generalizations have become a standard tool of infinite-dimensional analysis. They find applications in stochastic analysis, optimal transportation, mathematical physics, and mathematical finance.
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- Sobolev classes on infinite-dimensional spaces
Vladimir I. Bogachev
- Scuola Normale Superiore
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