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arXiv · 1611.00928

Stability of trace theorems on the sphere

Neal Bez·Chris Jeavons·Tohru Ozawa·Mitsuru Sugimoto
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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.

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Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto. 2016-11-03. Stability of trace theorems on the sphere. https://arxiv.org/abs/1611.00928

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