CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20170427-140719939

[img] PDF - Submitted Version
See Usage Policy.

214Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170427-140719939

Abstract

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jfa.2016.11.012DOIArticle
http://www.sciencedirect.com/science/article/pii/S0022123616303810PublisherArticle
https://arxiv.org/abs/1611.00462arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Subject Keywords:Resolvent; Laplace–Beltrami operator; Hadamard parametrix; Oscillatory integrals
Issue or Number:9
Record Number:CaltechAUTHORS:20170427-140719939
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170427-140719939
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, https://doi.org/10.1016/j.jfa.2016.11.012. (http://www.sciencedirect.com/science/article/pii/S0022123616303810)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77013
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:27 Apr 2017 21:44
Last Modified:03 Oct 2019 17:52

Repository Staff Only: item control page