Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds

Abstract

The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds, away from the endpoint regularity exponent. More generally, local smoothing estimates are established for a natural class of Fourier integral operators; at this level of generality the results are sharp in odd dimensions, both in terms of the regularity exponent and the Lebesgue exponent.

27 pages, 3 figures. Update incorporates referee suggestions. Minor correction to the proof of Lemma 2.6. To appear in APDE

References in corpus (2)

• Kakeya sets of curves
• On Instability of the Nikodym Maximal Function bounds over Riemannian Manifolds

Cited by in corpus (15)

• On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data
• $L^p$-Sobolev estimates for a class of integral operators with folding canonical relations
• Microlocal decoupling inequalities and the distance problem on Riemannian manifolds
• Local smoothing and Hardy spaces for Fourier integral operators
• Improved local smoothing estimate for the wave equation in higher dimensions
• Improved variable coefficient square functions and local smoothing of Fourier integral operators
• Nonlinear wave equations with slowly decaying initial data
• Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions
• Local smoothing for the Hermite wave equation
• Local smoothing and Hardy spaces for Fourier integral operators on manifolds
• Square function estimates and Local smoothing for Fourier Integral Operators
• $L^p({\mathbb{R}}^2)$-boundedness of Hilbert Transforms and Maximal Functions along Plane Curves with Two-variable Coefficients
• Hilbert transforms along variable planar curves: Lipschitz regularity
• $L^p-L^q$ estimates for the circular maximal operators on Heisenberg radial functions
• The Spherical Maximal Operators on Hyperbolic Spaces