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.
An extension problem for the CR fractional Laplacian / R.L. Frank, M.D.M. González, D.D. Monticelli, J. Tan. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 270:(2015 Jan 22), pp. 97-137. [10.1016/j.aim.2014.09.026]
An extension problem for the CR fractional Laplacian
D.D. MonticelliPenultimo
;
2015
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.
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