Boundedness of Fourier integral operators on classical function spaces

Abstract

We investigate the global boundedness of Fourier integral operators with amplitudes in the general Hörmander classes Sρ,δm(Rn), ρ,δ∈[0,1] and non-degenerate phase functions of arbitrary rank κ∈{0,1,…,n−1} on Besov-Lipschitz Bp,qs(Rn) and Triebel-Lizorkin Fp,qs(Rn) of order s and 0<p≤∞, 0<q≤∞. The results that are obtained are all up to the end-point and sharp and are also applied to the regularity of Klein-Gordon-type oscillatory integrals in the aforementioned function spaces.