Summary
We discuss Sobolev spaces of Banach-valued functions. They are extensions of Sobolev spaces of scalar functions. We use a gamma transform of a semigroup associated with a Markov process. A typical example is the Ornstein-Uhlenbeck process on the Wiener space.
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Shigekawa, I. Sobolev spaces of Banach-valued functions associated with a Markov process. Probab. Th. Rel. Fields 99, 425–441 (1994). https://doi.org/10.1007/BF01199900
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DOI: https://doi.org/10.1007/BF01199900
Mathematics Subject Classification
- 60H
- 60J