Sharp weighted CR trace Sobolev inequalities

Gunhee Cho; Zetian Yan

Sharp weighted CR trace Sobolev inequalities

Analysis of PDEs 2023-04-17 v1 Differential Geometry Functional Analysis

Authors: Gunhee Cho , Zetian Yan

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.

Keywords

sobolev inequalities sobolev spaces trace formula

Cite

@article{arxiv.2304.06874,
  title  = {Sharp weighted CR trace Sobolev inequalities},
  author = {Gunhee Cho and Zetian Yan},
  journal= {arXiv preprint arXiv:2304.06874},
  year   = {2023}
}

Comments

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

Sharp weighted CR trace Sobolev inequalities

Abstract

Keywords

Cite

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