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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 |
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Vol. 14 (2021), No. 1, 1–44
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Abstract |
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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 and certain Banach and quasi-Banach scales of Triebel–Lizorkin spaces . |
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Keywords
Besov–Lipschitz spaces, Triebel–Lizorkin spaces, Fourier
integral operators, hyperbolic equations
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Mathematical Subject Classification 2010
Primary: 35S30, 42B20, 35L05
Secondary: 35L15, 42B35
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Milestones
Received: 23 March 2018
Revised: 22 August 2019
Accepted: 20 December 2019
Published: 19 February 2021
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Authors |
| Anders Israelsson | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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| Salvador Rodríguez-López | |
| Department of Mathematics Stockholm University Stockholm Sweden |
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| Wolfgang Staubach | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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