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Endpoint resolvent estimates for compact Riemannian manifolds

Frank, Rupert L. and Schimmer, Lukas (2017) Endpoint resolvent estimates for compact Riemannian manifolds. Journal of Functional Analysis, 272 (9). pp. 3904-3918. ISSN 0022-1236. doi:10.1016/j.jfa.2016.11.012.

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We prove L^p→L^p′ bounds for the resolvent of the Laplace–Beltrami operator on a compact Riemannian manifold of dimension n in the endpoint case p=2(n+1)/(n+3). It has the same behavior with respect to the spectral parameter z as its Euclidean analogue, due to Kenig–Ruiz–Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.

Item Type:Article
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2016 Elsevier Inc. Received 2 November 2016. Accepted 30 November 2016. Available online 12 December 2016. Communicated by Daniel W. Stroock. The first author is partially supported by U.S. National Science Foundation grant DMS-1363432.
Funding AgencyGrant Number
Subject Keywords:Resolvent; Laplace–Beltrami operator; Hadamard parametrix; Oscillatory integrals
Issue or Number:9
Record Number:CaltechAUTHORS:20170427-140719939
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Official Citation:Rupert L. Frank, Lukas Schimmer, Endpoint resolvent estimates for compact Riemannian manifolds, Journal of Functional Analysis, Volume 272, Issue 9, 1 May 2017, Pages 3904-3918, ISSN 0022-1236, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77013
Deposited By: Ruth Sustaita
Deposited On:27 Apr 2017 21:44
Last Modified:15 Nov 2021 17:04

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