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

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Pseudo-Differential Operators and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 164))

Abstract

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.

This work was completed with the aid of UK-Japan Joint Project Grant by The Royal Society and Japan Society for the Promotion of Science.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College, 180 Queen’s Gate, London, SW7 2BZ, UK

    Michael Ruzhansky

  2. Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama-cho 1-16, Toyonaka, Osaka, 560-0043, Japan

    Mitsuru Sugimoto

Authors
  1. Michael Ruzhansky
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  2. Mitsuru Sugimoto
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, UniversitĂ  di Torino, Via Carlo Alberto, 10, 10123, Torino, Italy

    Paolo Boggiatto  & Luigi Rodino  & 

  2. School of Mathematics and Systems Engineering, Växjö University, SE-351 95, Växjö, Sweden

    Joachim Toft

  3. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Ruzhansky, M., Sugimoto, M. (2006). Global Calculus of Fourier Integral Operators, Weighted Estimates, and Applications to Global Analysis of Hyperbolic Equations. In: Boggiatto, P., Rodino, L., Toft, J., Wong, M.W. (eds) Pseudo-Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 164. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7514-0_5

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