Square function estimates and Local smoothing for Fourier Integral Operators

Abstract

We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is completely settled.

39 pages, 3 figures, Referees' suggestions incorporated. To appear in Proc. Lond. Math. Soc

References in corpus (3)

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
• A local smoothing estimate in higher dimensions
• Improved variable coefficient square functions and local smoothing of Fourier integral operators