Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of Fourier integral operators with amplitudes in general
  H\"ormander classes   We prove the global $L^p$-boundedness of Fourier integral operators that
model the parametrices for hyperbolic partial differential equations, with
amplitudes in classical H\"ormander classes $S^{m}_{\rho,
\delta}(\mathbb{R}^n)$ for parameters $0<\rho\leq 1$, $0\leq \delta<1$. We also
consider the regularity of operators with amplitudes in the exotic class
$S^{m}_{0, \delta}(\mathbb{R}^n)$, $0\leq \delta< 1$ and the forbidden class
$S^{m}_{\rho, 1}(\mathbb{R}^n)$, $0\leq\rho\leq 1.$ Furthermore we show that
despite the failure of the $L^2$-boundedness of operators with amplitudes in
the forbidden class $S^{0}_{1, 1}(\mathbb{R}^n)$, the operators in question are
bounded on Sobolev spaces $H^s(\mathbb{R}^n)$ with $s>0.$ This result extends
those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci