Published January 22, 2015
| Submitted
Journal Article
Open
An extension problem for the CR fractional Laplacian
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.Attached Files
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Additional details
- Eprint ID
- 55265
- DOI
- 10.1016/j.aim.2014.09.026
- Resolver ID
- CaltechAUTHORS:20150226-131020302
- PHY-1068285
- NSF
- PHY-1347399
- NSF
- MTM2011-27739-C04-01
- Spain Government
- GenCat 2009SGR345
- Spain Government
- 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"
- 1120105
- Chile Government Fondecyt
- USM 121402
- Chile Government Fondecyt
- Programa Basal
- Created
-
2015-02-26Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field