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arXiv · 2308.00973

Regularity of oscillatory integral operators

Anders Israelsson·Tobias Mattsson·Wolfgang Staubach
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Abstract

In this paper, we establish the global boundedness of oscillatory integral operators on Besov-Lipschitz and Triebel-Lizorkin spaces, with amplitudes in general $S^m_{\rho,\delta}(\mathbb{R}^n)$-classes and non-degenerate phase functions in the class $\textart F^k$. Our results hold for a wide range of parameters $0\leq\rho\leq1$, $0\leq\delta<1$, $0 0$. We also provide a sufficient condition for the boundedness of operators with amplitudes in the forbidden class $S^m_{1,1}(\mathbb{R}^n)$ in Triebel-Lizorkin spaces.

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Anders Israelsson, Tobias Mattsson, Wolfgang Staubach. 2023-08-02. Regularity of oscillatory integral operators. https://arxiv.org/abs/2308.00973

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