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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
Wolfgang Staubach Uppsala University , Uppsala , Sweden
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces
eBook ISBN:  978-1-4704-1528-0
Product Code:  MEMO/229/1074.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces
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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
Wolfgang Staubach Uppsala University , Uppsala , Sweden
eBook ISBN:  978-1-4704-1528-0
Product Code:  MEMO/229/1074.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2292013; 65 pp
    MSC: Primary 35; 42

    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
     
     
    • Chapters
    • Introduction
    • 1. Prolegomena
    • 2. Global Boundedness of Fourier Integral Operators
    • 3. Global and Local Weighted $L^p$ Boundedness of Fourier Integral Operators
    • 4. Applications in Harmonic Analysis and Partial Differential Equations
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2292013; 65 pp
MSC: Primary 35; 42

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.

  • Chapters
  • Introduction
  • 1. Prolegomena
  • 2. Global Boundedness of Fourier Integral Operators
  • 3. Global and Local Weighted $L^p$ Boundedness of Fourier Integral Operators
  • 4. Applications in Harmonic Analysis and Partial Differential Equations
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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