We prove the global \(L^p\)-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hörmander classes \(S^{m}_{\rho , \delta }(\mathbb {R}^n)\) for parameters \(0\le \rho \le 1\), \(0\le \delta <1\). We also consider the regularity of operators with amplitudes in the exotic class \(S^{m}_{0, \delta }(\mathbb {R}^n)\), \(0\le \delta < 1\) and the forbidden class \(S^{m}_{\rho , 1}(\mathbb {R}^n)\), \(0\le \rho \le 1.\) Furthermore we show that despite the failure of the \(L^2\)-boundedness of operators with amplitudes in the forbidden class \(S^{0}_{1, 1}(\mathbb {R}^n)\), the operators in question are bounded on Sobolev spaces \(H^s(\mathbb {R}^n)\) with \(s>0.\) This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.

我们证明了傅立叶积分算子的全局\(L^p\) 有界性，这些算子对双曲偏微分方程的参数进行建模，幅度在经典 Hörmander 类\(S^{m}_{\rho , \delta }(\ mathbb {R}^n)\)用于参数\(0\le \rho \le 1\)，\(0\le \delta <1\)。我们还考虑了奇异类中振幅算子的规律性\(S^{m}_{0, \delta }(\mathbb {R}^n)\) , \(0\le \delta < 1\)和禁止类\(S^{m}_{\rho , 1}(\mathbb {R}^n)\) , \(0\le \rho \le 1.\)此外我们表明，尽管失败所述的\（L ^ 2 \）-幅值在禁止类\(S^{0}_{1, 1}(\mathbb {R}^n)\)中的运算符的有界性，所讨论的运算符在 Sobolev 空间上有界\(H^s( \mathbb {R}^n)\)与\(s>0.\)这个结果将 Y. Meyer 和 EM Stein 的结果扩展到傅立叶积分算子的设置。