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.
ASJC Scopus subject areas
- Geometry and Topology