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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
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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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