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An extension problem for the CR fractional Laplacian

Frank, Rupert L. and González, María del Mar and Monticelli, Dario D. and Tan, Jinggang (2015) An extension problem for the CR fractional Laplacian. Advances in Mathematics, 270 . pp. 97-137. ISSN 0001-8708. https://resolver.caltech.edu/CaltechAUTHORS:20150226-131020302

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Abstract

We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre. We also prove an energy identity that yields a sharp trace Sobolev embedding.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.aim.2014.09.026DOIArticle
http://www.sciencedirect.com/science/article/pii/S0001870814003818PublisherArticle
http://arxiv.org/abs/1312.3381arXivDiscussion Paper
Additional Information:© 2014 Elsevier Inc. Received 17 December 2013, Accepted 5 September 2014, Available online 13 November 2014. Communicated by Charles Fefferman. R.F. acknowledges financial support from the NSF grants PHY-1068285 and PHY-1347399. M.G. was supported by Spain Government grant MTM2011-27739-C04-01 and GenCat 2009SGR345. D.M. was supported by GNAMPA project with title “Equazioni differenziali con invarianze in analisi globale”, by GNAMPA section “Equazioni differenziali e sistemi dinamici” and by MIUR project “Metodi variazionali e topologici nello studio di fenomeni nonlineari”. J.T. was supported by Chile Government grants Fondecyt #1120105, USM 121402, the Spain Government grant MTM2011-27739-C04-01 and Programa Basal, CMM. U. de Chile. The authors wish to thank the referee for many useful comments which helped in the exposition.
Funders:
Funding AgencyGrant Number
NSFPHY-1068285
NSFPHY-1347399
Spain GovernmentMTM2011-27739-C04-01
Spain GovernmentGenCat 2009SGR345
GNAMPA project “Equazioni differenziali con invarianze in analisi globale”UNSPECIFIED
GNAMPA section “Equazioni differenziali e sistemi dinamici”UNSPECIFIED
MIUR project “Metodi variazionali e topologici nello studio di fenomeni nonlineari”UNSPECIFIED
Chile Government Fondecyt1120105
Chile Government FondecytUSM 121402
Programa BasalUNSPECIFIED
Subject Keywords:Fractional order operators; Fractional order weighted Sobolev spaces; Sublaplacian; CR manifolds; Heisenberg group
Record Number:CaltechAUTHORS:20150226-131020302
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150226-131020302
Official Citation:Rupert L. Frank, María del Mar González, Dario D. Monticelli, Jinggang Tan, An extension problem for the CR fractional Laplacian, Advances in Mathematics, Volume 270, 22 January 2015, Pages 97-137, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2014.09.026. (http://www.sciencedirect.com/science/article/pii/S0001870814003818)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55265
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Feb 2015 22:23
Last Modified:03 Oct 2019 08:04

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