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

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove stable versions of trace theorems on the sphere in L² 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.

Original language	English
Pages (from-to)	1456-1476
Number of pages	21
Journal	Journal of Geometric Analysis
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s12220-017-9870-8
Publication status	Published - 2018 Apr 1

Keywords

Duality
Stability estimates
Trace theorems

ASJC Scopus subject areas

Geometry and Topology

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title = "Stability of Trace Theorems on the Sphere",

abstract = "We prove stable versions of trace theorems on the sphere in L2 with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into Lq 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{\textquoteright}s duality theorem to establish local stability of certain Strichartz estimates for the kinetic transport equation.",

keywords = "Duality, Stability estimates, Trace theorems",

author = "Neal Bez and Chris Jeavons and Tohru Ozawa and Mitsuru Sugimoto",

note = "Funding Information: Acknowledgements This work was supported by the JSPS Grant-in-Aid for Young Scientists A No. 16H05995 (Bez), by the JSPS KAKENHI 26287022 and 26610021 (Sugimoto), and by the JSPS Fellowship for Overseas Researchers FY 2015-2016 (Jeavons, Ozawa).",

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T1 - Stability of Trace Theorems on the Sphere

AU - Bez, Neal

AU - Jeavons, Chris

AU - Ozawa, Tohru

AU - Sugimoto, Mitsuru

N1 - Funding Information: Acknowledgements This work was supported by the JSPS Grant-in-Aid for Young Scientists A No. 16H05995 (Bez), by the JSPS KAKENHI 26287022 and 26610021 (Sugimoto), and by the JSPS Fellowship for Overseas Researchers FY 2015-2016 (Jeavons, Ozawa).

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We prove stable versions of trace theorems on the sphere in L2 with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into Lq 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.

AB - We prove stable versions of trace theorems on the sphere in L2 with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into Lq 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.

KW - Duality

KW - Stability estimates

KW - Trace theorems

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