Regularity of oscillatory integral operators

In this paper, we establish the global boundedness of oscillatory integral operators on Besov–Lipschitz and Triebel–Lizorkin spaces, with amplitudes in general [Formula: see text]-classes and non-degenerate phase functions in the class ᚠ k . Our results hold for a wide range of parameters [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We also provide a sufficient condition for the boundedness of operators with amplitudes in the forbidden class [Formula: see text] in Triebel–Lizorkin spaces.