Stability of Trace Theorems on the Sphere

Neal Bez; Chris Jeavons; Tohru Ozawa; Mitsuru Sugimoto

doi:10.1007/s12220-017-9870-8

Stability of Trace Theorems on the Sphere

Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

We prove stable versions of trace theorems on the sphere in (Formula presented.) with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into (Formula presented.) for (Formula presented.), 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.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of Geometric Analysis
DOIs	https://doi.org/10.1007/s12220-017-9870-8
Publication status	Accepted/In press - 2017 Jun 1

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Keywords

Duality
Stability estimates
Trace theorems

ASJC Scopus subject areas

Geometry and Topology

Cite this

Bez, N., Jeavons, C., Ozawa, T., & Sugimoto, M. (Accepted/In press). Stability of Trace Theorems on the Sphere. Journal of Geometric Analysis, 1-21. https://doi.org/10.1007/s12220-017-9870-8

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10.1007/s12220-017-9870-8