Local and global estimates for hyperbolicequations in Besov–Lipschitz and Triebel–Lizorkin spaces
Anders Wimo, Salvador Rodríguez-López, Wolfgang Staubach
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 $B^s_{p,q}(\R^n)$, and certain Banach and quasi-Banach scales of Triebel-Lizorkin spaces $F^s_{p,q}(\R^n)$
Topics & Concepts
Lipschitz continuityMathematicsBanach spaceBesov spacePure mathematicsMathematical analysisInterpolation spaceFunctional analysisChemistryGeneBiochemistryAdvanced Harmonic Analysis ResearchAdvanced Mathematical Physics ProblemsDifferential Equations and Boundary Problems