Let $T_{a,\varphi }$ be a Fourier integral operator with symbol a and phase φ. In this paper, under the conditions $a(x,\xi )\in L^{\infty }S^{n(\rho -1)/2}_{\rho }(\omega )$ and $\varphi \in L^{\infty }\varPhi ^{2}$, the authors show that $T_{a,\varphi }$ is bounded from $L^{2}(\mathbb{R}^{n})$ to $L^{2}(\mathbb{R}^{n})$.

中文翻译：

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关于傅立叶积分算子的\（L ^ {2} \）有界

令$ T_ {a，\ varphi} $为傅立叶积分算符，其符号为a，相位为。本文在$ a（x，\ xi）\ in L ^ {\ infty} S ^ {n（\ rho -1）/ 2} _ {\ rho}（\ omega）$和$ \ varphi条件下\ in L ^ {\ infty} \ varPhi ^ {2} $，作者表明$ T_ {a，\ varphi} $受$ L ^ {2}（\ mathbb {R} ^ {n}）$的限制到$ L ^ {2}（\ mathbb {R} ^ {n}）$。