Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spaces

Abstract

In this paper 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 $B_{p,q}^s({\mathbb{R}}^n)$, and certain Banach and quasi-Banach scales of Triebel-Lizorkin spaces $F_{p,q}^s({\mathbb{R}}^n)$

arXiv comment47 pages, 1 figure

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Cited by in corpus (2)

• Regularity of Fourier integral operators with amplitudes in general Hörmander classes
• Regularity properties of Schrödinger integral operators and general oscillatory integrals