Pseudo-Differential Operators and Related Topics

Volume 164 of the series Operator Theory: Advances and Applications pp 65-78

Global Calculus of Fourier Integral Operators, Weighted Estimates, and Applications to Global Analysis of Hyperbolic Equations

  • Michael RuzhanskyAffiliated withDepartment of Mathematics, Imperial College
  • , Mitsuru SugimotoAffiliated withDepartment of Mathematics, Graduate School of Science, Osaka University

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The aim of this paper is to present certain global regularity properties of hyperbolic equations. In particular, it will be determined in what way the global decay of Cauchy data implies the global decay of solutions. For this purpose, global weighted estimates in Sobolev spaces for Fourier integral operators will be reviewed. We will also present elements of the global calculus under minimal decay assumptions on phases and amplitudes.


Fourier integral operators hyperbolic equations global estimates