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 |
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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 229; 2013; 65 ppMSC: 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.
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Table of Contents
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Chapters
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Introduction
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1. Prolegomena
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2. Global Boundedness of Fourier Integral Operators
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3. Global and Local Weighted $L^p$ Boundedness of Fourier Integral Operators
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4. Applications in Harmonic Analysis and Partial Differential Equations
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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.
-
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