Abstract
In this paper, we establish the \(L^{p}\)-boundedness of Fourier integral operators \(T_{\phi ,a}\) with rough amplitude and phase function, which satisfies the new class of rough non-degeneracy condition. In this study, under the conditions \(a\in L^{\infty }S^{m}_{\rho }\), \({\phi }\in L^{\infty }\Phi ^{2}\) and when \( 1-\frac{\delta }{2}\leqslant \rho \le 1\), we show that \(T_{\phi ,a}\) is bounded from \(L^{p}\) to itself for \(p\in [1,\infty ]\) with some measure conditions on m. Our main results extend and improve some known results about \(L^{p}\)-boundedness of Fourier integral operators.
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Sindayigaya, J. Global \(L^{p}\)-Boundedness of Rough Fourier Integral Operators. Mediterr. J. Math. 20, 241 (2023). https://doi.org/10.1007/s00009-023-02448-5
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DOI: https://doi.org/10.1007/s00009-023-02448-5