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Published January 22, 2015 | Version Submitted
Journal Article Open

An extension problem for the CR fractional Laplacian

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Universitat Politècnica de Catalunya
  • 3. ROR icon University of Milan
  • 4. ROR icon Federico Santa María Technical University

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.

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.

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Additional details

Identifiers

Eprint ID
55265
DOI
10.1016/j.aim.2014.09.026
Resolver ID
CaltechAUTHORS:20150226-131020302

Related works

Describes
10.1016/j.aim.2014.09.026 (DOI)
http://arxiv.org/abs/1312.3381 (URL)

Funding

NSF
PHY-1068285
NSF
PHY-1347399
Spain Government
MTM2011-27739-C04-01
Spain Government
GenCat 2009SGR345
GNAMPA project "Equazioni differenziali con invarianze in analisi globale"
GNAMPA section "Equazioni differenziali e sistemi dinamici"
MIUR project "Metodi variazionali e topologici nello studio di fenomeni nonlineari"
Chile Government Fondecyt
1120105
Chile Government Fondecyt
USM 121402
Programa Basal

Dates

Created
2015-02-26
Created from EPrint's datestamp field
Updated
2021-11-10
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Mathematics Department