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Sobolev spaces of Banach-valued functions associated with a Markov process
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  • Published: September 1994

Sobolev spaces of Banach-valued functions associated with a Markov process

  • Ichiro Shigekawa1 

Probability Theory and Related Fields volume 99, pages 425–441 (1994)Cite this article

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan

    Ichiro Shigekawa

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  1. Ichiro Shigekawa
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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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  • Received: 07 June 1993

  • Revised: 21 December 1993

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01199900

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  • 60H
  • 60J
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