An extension problem for the CR fractional Laplacian

By Rupert L. Frank, Mar'ia de Mar Gonz'alez, D. Monticelli, Jinggang Tan. 2013

91 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9b1d50ea89bd167c75d9d3535f7721f5af920501

Citations in the corpus

• Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, unknown): “They also arise in connection with the extension problem on the Heisenberg group as expounded in the recent work of Frank et al [19].”