\(L_p\)-\(L_{p'}\)-estimates for Fourier integral operators related to hyperbolic equations

DOI10.1007/BF01488969zbMath0325.35009MaRDI QIDQ1225227

Philip Brenner

Publication date: 1977

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172472

zbMATH Keywords

existenceuniquenessFourier integral operatorsa-priori estimatessemilinear hyperbolic equations with variable coefficients

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) A priori estimates in context of PDEs (35B45) Fourier integral operators applied to PDEs (35S30)

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Bounds for singular fractional integrals and related Fourier integral operators ⋮ Strichartz Estimates for Non-selfadjoint Operators and Applications ⋮ Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces ⋮ 𝐿^{𝑝}→𝐿^{𝑞} regularity of Fourier integral operators with caustics ⋮ Asymptotic behavior of waves ⋮ Blow-up of solutions to critical semilinear wave equations with variable coefficients ⋮ Two endpoint bounds for generalized Radon transforms in the plane ⋮ The lifespan of solutions to nonlinear systems of a high-dimensional wave equation ⋮ Uniqueness in Cauchy Problems for Hyperbolic Differential Operators ⋮ Estimates for the wave kernel near focal points on compact manifolds ⋮ Decay Estimates for the Wave Equation with Potential ⋮ Norm estimates in Besov and Lizorkin-Triebel spaces for the solutions of second-order linear hyperbolic equations ⋮ Sharp \(L^p\)-Carleman estimates and unique continuation

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