Stability of Trace Theorems on the Sphere

• Bez, Neal

• Jeavons, Chris

• Ozawa, Tohru

• Sugimoto, Mitsuru

Abstract

We prove stable versions of trace theorems on the sphere in L^2 with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into L^q for q>2, by combining a refined Hardy–Littlewood–Sobolev inequality on the sphere with a duality–stability result proved very recently by Carlen. Finally, we extend a local version of Carlen’s duality theorem to establish local stability of certain Strichartz estimates for the kinetic transport equation.

Journal

• The Journal of Geometric Analysis

  The Journal of Geometric Analysis 28 (2), 1456-1476, 2018-04

  Springer

Keywords

• Trace theorems
• Stability estimates
• Duality

Details

• CRID: 1050282813783570304
• NII Article ID: 120006496423
• DOI: 10.1007/s12220-017-9870-8
• ISSN: 1559002X
• ISSN: 10506926
• HANDLE: 2237/00028451
• Web Site: https://nagoya.repo.nii.ac.jp/records/26247
• Web Site: http://link.springer.com/article/10.1007/s12220-017-9870-8/fulltext.html
• Web Site: http://link.springer.com/content/pdf/10.1007/s12220-017-9870-8.pdf
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN