$L^p - L^q$ resolvent restriction estimates for submanifolds

TL;DR

This paper investigates restriction estimates for hypersurfaces related to Sobolev inequalities and resolvent estimates, extending known results in harmonic analysis and PDEs to new settings.

Contribution

It introduces new $L^p - L^q$ resolvent restriction estimates for submanifolds, expanding the understanding of restriction phenomena in harmonic analysis.

Findings

Established new restriction estimates for hypersurfaces.

Extended Sobolev and resolvent inequalities to submanifolds.

Provided applications to PDEs and harmonic analysis.

Abstract

We consider restriction analogues on hypersurfaces of the uniform Sobolev inequalities in Kenig, Ruiz, and Sogge and the resolvent estimates in Dos Santos Ferreira, Kenig, and Salo.