On some \(L^ p\)-estimates for hyperbolic equations

DOI10.1007/BF02384867zbMath0764.35057MaRDI QIDQ1197464

Mitsuru Sugimoto

Publication date: 16 January 1993

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

Fourier transformSobolev spacesSchrödinger equationsBesov spacessolutions of Cauchy problems

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Initial value problems for higher-order hyperbolic equations (35L30) Equations in function spaces; evolution equations (58D25) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items

A local-to-global boundedness argument and Fourier integral operators ⋮ \(L^p-L^q\) estimates for higher order perturbed hyperbolic equation ⋮ Sharp estimates for a class of hyperbolic pseudo-differential equations ⋮ Representation of Schrödinger operator of a free particle via short-time Fourier transform and its applications ⋮ Global $L^p$ continuity of Fourier integral operators ⋮ On Local and Global Regularity of Fourier Integral Operators ⋮ A priori estimates for higher order hyperbolic equations

Cites Work

• \(L^p\) estimates for the waves equation
• Regularity properties of Fourier integral operators
• Fourier integral operators. I
• \(H^p\) spaces of several variables
• Differential forms. With applications to the physical sciences
• Estimates for Solutions of Wave Equations with Vanishing Curvature
• A characterization of $H^{p}(R^{n})$ in terms of atoms
• 𝐿^{𝑝} boundedness of Fourier integral operators
• Special trigonometric series in 𝑘-dimensions
• On multiplier transformations
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