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Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces
David Dos Santos Ferreira, Université Paris 13, Villetaneuse, France, and Wolfgang Staubach, Uppsala University, Sweden

Memoirs of the American Mathematical Society
2013; 65 pp; softcover
Volume: 229
ISBN-10: 0-8218-9119-7
ISBN-13: 978-0-8218-9119-3
List Price: US$63
Individual Members: US$37.80
Institutional Members: US$50.40
Order Code: MEMO/229/1074
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The authors investigate the global continuity on \(L^p\) spaces with \(p\in [1,\infty]\) of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global \(L^2\) boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in \(S^{m} _{\varrho, \delta}\) with \(\varrho , \delta \in [0,1]\). They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted \(L^{p}\) spaces, \(L_{w}^p\) with \(1< p < \infty\) and \(w\in A_{p},\) (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.

Table of Contents

  • Prolegomena
  • Global boundedness of Fourier integral operators
  • Global and local weighted \(L^p\) boundedness of Fourier integral operators
  • Applications in harmonic analysis and partial differential equations
  • Bibliography
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