Abstract
We establish a family of sharp Sobolev trace inequalities involving the Wk,2(R+n+1,ya)-norm. These inequalities are closely related to the realization of fractional powers of the Laplacian on Rn=∂R+n+1 as generalized Dirichlet-to-Neumann operators associated to powers of the weighted Laplacian in upper half space, generalizing observations of Caffarelli–Silvestre and of Yang.
Original language | English (US) |
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Article number | 108567 |
Journal | Journal of Functional Analysis |
Volume | 279 |
Issue number | 4 |
DOIs | |
State | Published - Sep 1 2020 |
All Science Journal Classification (ASJC) codes
- Analysis