A Sobolev estimate for the adjoint restriction operator

Abstract

In this note we consider the adjoint restriction estimate for hypersurface under additional regularity assumption. We obtain the optimal $H^s$-$L^q$ estimate and its mixed norm generalization. As applications we prove some weighted Strichartz estimates for the propagator $e^{it(-\Delta {)}^{\alpha /2}}\phi$, $\alpha >0$.

14 pages, 0 figure; correct some typos; to appear Math. Ann

References in corpus (2)

• Generalized and weighted Strichartz estimates
• Strichartz Estimates in Spherical Coordinates