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Sharp weighted CR trace Sobolev inequalities (2304.06874v1)
Published 14 Apr 2023 in math.AP, math.DG, and math.FA
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 $Hn=\partial \Omega_{n+1}$ as generalized Dirichlet-to-Neumann operators associated to the weighted poly-sublaplacian, generalizing observations of Frank--Gonz\'alez--Monticelli--Tan.