关键词: Fourier integral operators, phase function, BMO spaces

Abstract: Let $T_{a,\varphi}$ be a Fourier integral operator defined by the oscillatory integral \begin{eqnarray*} T_{a,\varphi}u(x) &=&\frac{1}{(2\pi)^n}\int_{\mathbb{R}^n} e^{ {\rm i} \varphi(x,\xi)}a(x,\xi) \hat{u}(\xi){\rm d}\xi, \end{eqnarray*} where $a\in S^{m}_{\varrho,\delta}$ and $\varphi\in \Phi^{2}$, satisfying the strong non-degenerate condition. It is shown that if $0<\varrho\leq1$, $0\leq\delta<1$ and $m\leq \frac{\varrho^{2}-n}{2}$, then $T_{a,\varphi}$ is a bounded operator from $L^{\infty}(\mathbb{R}^n)$ to ${\rm BMO}(\mathbb{R}^n).$

Key words: Fourier integral operators, phase function, BMO spaces