Remarks on Wolff's inequality for hypersurfaces

TL;DR

This paper extends sharp decoupling inequalities to conical surfaces and k-cones using an iteration argument, advancing the understanding of Fourier analysis on hypersurfaces.

Contribution

It provides a new proof of sharp decoupling inequalities for conical surfaces and k-cones, extending previous results to sharp exponents.

Findings

Established sharp decoupling inequalities for conical surfaces.

Extended results of ba and Pramanik to sharp exponents.

Utilized an iteration argument by Pramanik and Seeger.

Abstract

We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$-cones. These are extensions of results \L aba and Pramanik to sharp exponents.