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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

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.

• Global and local weighted $$L^p$$ boundedness of Fourier integral operators