Off-singularity bounds and Hardy spaces for Fourier integral operators

Abstract

We define a scale of Hardy spaces ${\mathcal{H}}_{FIO}^p({\mathbb{R}}^n)$, $p\in [1,\infty ]$, that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for $p=1$. We also introduce a notion of off-singularity decay for kernels on the cosphere bundle of ${\mathbb{R}}^n$, and we combine this with wave packet transforms and tent spaces over the cosphere bundle to develop a full Hardy space theory for oscillatory integral operators. In the process we extend the known results about $L^p$-boundedness of Fourier integral operators, from local boundedness to global boundedness for a larger class of symbols.

59 pages. Final version before publication

Cited by in corpus (9)

• Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spaces
• Regularity of Fourier integral operators with amplitudes in general Hörmander classes
• Local smoothing and Hardy spaces for Fourier integral operators
• Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II
• $L^p$ and ${\mathcal{H}}_{FIO}^p$ regularity for wave equations with rough coefficients
• Nonlinear wave equations with slowly decaying initial data
• Rough pseudodifferential operators on Hardy spaces for Fourier integral operators
• Local smoothing and Hardy spaces for Fourier integral operators on manifolds
• Function spaces for decoupling