Off-Singularity bounds and hardy spaces for fourier integral operators

We define a scale of Hardy spaces Hp FIO(Rn), p ∈ [1,∞], that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for p = 1 [J. Geom. Anal. 8 (1998), pp. 629-653]. We also introduce a notion of off-singularity decay for kernels on the cosphere bundle of Rn, 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 Lp-boundedness of Fourier integral operators, from local boundedness to global boundedness for a larger class of symbols.