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 languageEnglish
    Pages (from-to)1-21
    Number of pages21
    JournalJournal of Geometric Analysis
    DOIs
    Publication statusAccepted/In press - 2017 Jun 1

    Keywords

    • Duality
    • Stability estimates
    • Trace theorems

    ASJC Scopus subject areas

    • Geometry and Topology

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