Sharp weighted CR trace Sobolev inequalities

Gunhee Cho; Zetian Yan

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arXiv · 2304.06874

Sharp weighted CR trace Sobolev inequalities

Gunhee Cho·Zetian Yan

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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--Gonz\'alez--Monticelli--Tan.

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Gunhee Cho, Zetian Yan. 2023-04-14. Sharp weighted CR trace Sobolev inequalities. https://arxiv.org/abs/2304.06874

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