Sharp weighted CR trace Sobolev inequalities

Abstract

We establish a sharp Sobolev trace inequality on the Siegel domain ${\Omega }_{n+1}$ involving the weighted norm-$W^{2,2}({\Omega }_{n+1},{\rho }^{1-2[\gamma ]})$. The inequality is closely related the realization of fractional powers of the sub-Laplacian on the Heisenberg group $H^n=\partial {\Omega }_{n+1}$ as generalized Dirichlet-to-Neumann operators associated to the weighted poly-sublaplacian, generalizing observations of Frank--González--Monticelli--Tan.

25 pages; a new sharp weighted CR trace Sobolev inequality on Siegel domain. arXiv admin note: text overlap with arXiv:1901.09843 by other authors