Stability of trace theorems on the sphere

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.

arXiv comment18 pages

References in corpus (7)

• Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
• A stability version of Hölder's inequality
• A sharpened Hausdorff-Young inequality
• Near-extremizers of Young's Inequality for R^d
• Optimal constants and extremisers for some smoothing estimates
• Trace theorems: critical cases and best constants
• Periodic motions generated from non-autonomous grazing dynamics

Cited by in corpus (2)

• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for $L^p$-weighted Hardy inequalities
• A note on stability of Hardy inequalities