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].