Vol. 14, No. 1, 2021

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

Anders Israelsson, Salvador Rodríguez-López and Wolfgang Staubach

Vol. 14 (2021), No. 1, 1–44
Abstract

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 ${F}_{p,q}^{s}\left({ℝ}^{n}\right)$.

Keywords
Besov–Lipschitz spaces, Triebel–Lizorkin spaces, Fourier integral operators, hyperbolic equations
Mathematical Subject Classification 2010
Primary: 35S30, 42B20, 35L05
Secondary: 35L15, 42B35
Milestones
Revised: 22 August 2019
Accepted: 20 December 2019
Published: 19 February 2021
Authors
 Anders Israelsson Department of Mathematics Uppsala University Uppsala Sweden Salvador Rodríguez-López Department of Mathematics Stockholm University Stockholm Sweden Wolfgang Staubach Department of Mathematics Uppsala University Uppsala Sweden