Local smoothing and Hardy spaces for Fourier integral operators on manifolds

Abstract

We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic curvature condition, and for wave equations on compact manifolds. The estimates are essentially sharp, for all $2<p<\infty$ and on each compact manifold. We also apply our local smoothing estimates to nonlinear wave equations with initial data outside of $L^2$-based Sobolev spaces.

Section 2 moved to Appendix A, additional minor changes. To appear in Journal of Functional Analysis. 57 pages

References in corpus (4)

• On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data
• Local smoothing and Hardy spaces for Fourier integral operators
• Maximal characterisation of local Hardy spaces on locally doubling manifolds
• Nonlinear wave equations with slowly decaying initial data