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An extension problem,
trace Hardy and Hardy's inequalities for the
Ornstein–Uhlenbeck operator
Pritam Ganguly, Ramesh Manna and Sundaram Thangavelu |
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Vol. 16 (2023), No. 5, 1205–1244
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Abstract |
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We study an extension problem for the Ornstein–Uhlenbeck operator , and we obtain various characterisations of the solution of the same. We use a particular solution of that extension problem to prove a trace Hardy inequality for from which Hardy’s inequality for fractional powers of is obtained. We also prove an isometry property of the solution operator associated to the extension problem. Moreover, new estimates are obtained for the fractional powers of the Hermite operator. |
Keywords
extension problem, trace Hardy inequality, Hardy's
inequality, Ornstein–Uhlenbeck operator
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Mathematical Subject Classification
Primary: 26D10, 35J15
Secondary: 26A33, 33C45, 35A23, 43A80
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Milestones
Received: 17 December 2020
Revised: 19 September 2021
Accepted: 28 October 2021
Published: 12 August 2023
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Authors |
| Pritam Ganguly | |
| Institut für Mathematik Universität Paderborn Paderborn Germany |
Department of Mathematics Indian Institute of Science Bangalore India |
| Ramesh Manna | |
| School of Mathematical
Sciences National Institute of Science Education and Research Bhubaneswar an OCC of Homi Bhabha National Institute Jatni, 752050 India |
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| Sundaram Thangavelu | |
| Department of Mathematics Indian Institute of Science Bangalore India |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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