An extension problem for the CR fractional Laplacian

An extension problem for the CR fractional Laplacian

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 Caffarell...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) Vol. 270; pp. 97 - 137
Main Authors: Frank, Rupert L., González, María del Mar, Monticelli, Dario D., Tan, Jinggang
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 22-01-2015
Subjects:
CR manifolds
Differential geometry
Fractional order operators
Fractional order weighted Sobolev spaces
Geometria diferencial
Heisenberg group
Sublaplacian
Heisenberg group
Fractional order weighted Sobolev spaces
Sublaplacian
CR manifolds
Fractional order operators
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2014.09.026