Local smoothing and Hardy spaces for Fourier integral operators

Abstract

We show that the Hardy spaces for Fourier integral operators form natural spaces of initial data when applying ${\ell }^p$-decoupling inequalities to local smoothing for the wave equation. This yields new local smoothing estimates which, in a quantified manner, improve the bounds in the local smoothing conjecture on ${\mathbb{R}}^n$ for $p\ge 2(n+1)/(n-1)$, and complement them for $2<p<2(n+1)/(n-1)$. These estimates are invariant under application of Fourier integral operators, and they are essentially sharp.

Final version before publication, to appear in Journal of Functional Analysis. 17 pages

References in corpus (4)

• Global and local regularity of Fourier integral operators on weighted and unweighted spaces
• On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data
• Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II
• Nonlinear wave equations with slowly decaying initial data

Cited by in corpus (3)

• Nonlinear wave equations with slowly decaying initial data
• Local smoothing and Hardy spaces for Fourier integral operators on manifolds
• Function spaces for decoupling