On \(L^{2}\) -boundedness of Fourier integral operators

[摘要] 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 $L^{2}(\mathbb{R}^{n})$.

[学科分类] 电力

[关键词] Pseudo-differential operator;Fourier integral operator;Phase function