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

Journal of inequalities and applications

article

Jie Yang¹  Wenyi Chen²  Jiang Zhou¹ 

[1] College of Mathematics and System Science, Xinjiang University;School of Mathematics and Statistics, Wuhan University

关键词: Pseudo-differential operator;    Fourier integral operator;    Phase function;   

DOI  :  10.1186/s13660-020-02439-0

学科分类：电力

来源: SpringerOpen

【 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 $L^{2}(\mathbb{R}^{n})$.

【 授权许可】

CC BY