Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian

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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 languageEnglish (US)
Article number108567
JournalJournal of Functional Analysis
Volume279
Issue number4
DOIs
StatePublished - Sep 1 2020

All Science Journal Classification (ASJC) codes

  • Analysis

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