Notes on Regularity of Fourier integral operators with symbol in S0,δm

Let Formula: see text be a Fourier integral operator defined with Formula: see text and Formula: see text satisfying the strong non-degenerate condition. We demonstrate that when the order satisfies Formula: see text the operator Formula: see text becomes bounded on Formula: see text for Formula: see text and maps Formula: see text to Formula: see text when Formula: see text. Furthermore, the derived bound on Formula: see text is sharp for Formula: see text estimates in the case Formula: see text, and for Formula: see text when Formula: see text.