{"paper":{"title":"Fourier integral operators on Hardy spaces with Hormander class","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chunjie Zhang, Xiangrong Zhu, Xiaofeng Ye","submitted_at":"2024-06-05T08:59:47Z","abstract_excerpt":"In this note, we consider a Fourier integral operator defined by \\begin{align*} T_{\\phi,a}f(x) = \\int_{\\mathbb{R}^{n}}e^{i\\phi(x,\\xi)}a(x,\\xi)\\widehat{f} \\xi)d\\xi, \\end{align*}here $a$ is the amplitude, and $\\phi$ is the phase. Let $0\\leq\\rho\\leq 1,n\\geq 2$ or $0\\leq\\rho<1,n=1$ and $$m_p=\\frac{\\rho-n}{p}+(n-1)\\min\\{\\frac 12,\\rho\\}.$$ If $a$ belongs to the forbidden H\\\"{o}rmander class $S^{m_p}_{\\rho,1}$ and $\\phi\\in \\Phi^{2}$ satisfies the strong non-degeneracy condition, then for any $\\frac {n}{n+1}