We establish optimal local and global Besov–Lipschitz and Triebel–Lizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier integral operators that span all possible scales (and in particular both Banach and quasi-Banach scales) of Besov–Lipschitz spaces $B_{p,q}^s\left({ℝ}^n\right)$ and certain Banach and quasi-Banach scales of Triebel–Lizorkin spaces $F_{p,q}^s\left({ℝ}^n\right)$.

中文翻译：

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Besov–Lipschitz和Triebel–Lizorkin空间中双曲方程的局部和全局估计

我们为线性双曲型偏微分方程的解建立了最优的局部和全局Besov-Lipschitz和Triebel-Lizorkin估计。这些估计是基于对Besov–Lipschitz空间的所有可能尺度（尤其是Banach和准Banach尺度）的Fourier积分算子的局部和全局估计。${乙}_{p，q}^s（{ℝ}^{ñ}）$ 以及Triebel–Lizorkin空间的某些Banach和准Banach尺度 $F_{p，q}^s（{ℝ}^{ñ}）$。