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.

18 pages

References in corpus (4)

• A stability version of Hölder's inequality
• A sharpened Hausdorff-Young inequality
• Optimal constants and extremisers for some smoothing estimates
• Periodic motions generated from non-autonomous grazing dynamics

Cited by in corpus (1)

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