Sharp trace inequalities for fractional Laplacians

Einav, Amit; Loss, Michael

Abstract

The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rn, and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s sharp form of the Hardy-Littlewood-Sobolev inequality.

Citation

Einav, A., & Loss, M. (2012). Sharp trace inequalities for fractional Laplacians. Proceedings of the American Mathematical Society, 140(12), https://doi.org/10.1090/s0002-9939-2012-11380-2

• Journal Article Type: Article
• Acceptance Date: Mar 5, 2012
• Online Publication Date: Apr 5, 2012
• Publication Date: 2012
• Deposit Date: Nov 16, 2020
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Volume: 140
• Issue: 12
• DOI: https://doi.org/10.1090/s0002-9939-2012-11380-2
• Public URL: https://durham-repository.worktribe.com/output/1257236