### Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces

Hinz M, Kang S (2020)
Potential Analysis.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Autor*in
Hinz, MichaelUniBi; Kang, Seunghyun
Einrichtung
Abstract / Bemerkung
We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for theL(p)-uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions vanishing in a neighborhood of a given closed set sigma of zero Gaussian measure. To prove the equivalence we show theW(r,p)(B,mu)-boundedness of certain smooth nonlinear truncation operators acting on potentials of nonnegative functions. We discuss connections to Gaussian Hausdorff measures. Roughly speaking, ifL(p)-uniqueness holds then the 'removed' set sigma must have sufficiently large codimension, in the case of the Ornstein-Uhlenbeck operator for instance at least 2p. Forp= 2 we obtain parallel results on truncations, capacities and essential self-adjointness for Ornstein-Uhlenbeck operators with linear drift. These results apply to the time zero Gaussian free field as a prototype example.
Stichworte
Wiener spaces; Capacities; Ornstein-Uhlenbeck operator; Sobolev spaces; Composition operators; L-p-uniqueness
Erscheinungsjahr
2020
Zeitschriftentitel
Potential Analysis
ISSN
0926-2601
eISSN
1572-929X
Page URI
https://pub.uni-bielefeld.de/record/2945843

### Zitieren

Hinz M, Kang S. Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis. 2020.
Hinz, M., & Kang, S. (2020). Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis. doi:10.1007/s11118-020-09836-6
Hinz, M., and Kang, S. (2020). Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis.
Hinz, M., & Kang, S., 2020. Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis.
M. Hinz and S. Kang, “Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces”, Potential Analysis, 2020.
Hinz, M., Kang, S.: Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis. (2020).
Hinz, Michael, and Kang, Seunghyun. “Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces”. Potential Analysis (2020).
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Open Access