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

Hinz M, Kang S (2021)
Potential Analysis 54: 503–533.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Hinz, MichaelUniBi; Kang, Seunghyun
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
2021
Zeitschriftentitel
Potential Analysis
Band
54
Seite(n)
503–533
ISSN
0926-2601
eISSN
1572-929X
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2945843

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Hinz M, Kang S. Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis. 2021;54:503–533.
Hinz, M., & Kang, S. (2021). Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis, 54, 503–533. https://doi.org/10.1007/s11118-020-09836-6
Hinz, M., and Kang, S. (2021). Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis 54, 503–533.
Hinz, M., & Kang, S., 2021. Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis, 54, p 503–533.
M. Hinz and S. Kang, “Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces”, Potential Analysis, vol. 54, 2021, pp. 503–533.
Hinz, M., Kang, S.: Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces. Potential Analysis. 54, 503–533 (2021).
Hinz, Michael, and Kang, Seunghyun. “Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces”. Potential Analysis 54 (2021): 503–533.
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2021-03-05T13:10:36Z
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