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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Global $ L^p$ continuity of Fourier integral operators


Authors: Sandro Coriasco and Michael Ruzhansky
Journal: Trans. Amer. Math. Soc. 366 (2014), 2575-2596
MSC (2010): Primary 35S30; Secondary 42B30, 46E30, 47B34
Published electronically: January 13, 2014
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Abstract: In this paper we establish global $ L^p(\mathbb{R}^{n})$-regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on $ L^p(\mathbb{R}^{n})$, $ 1<p<\infty $, as well as to be bounded from Hardy space $ H^1(\mathbb{R}^{n})$ to $ L^1(\mathbb{R}^{n})$. This extends local $ L^p$-regularity properties of Fourier integral operators, as well as results of global $ L^2(\mathbb{R}^{n})$ boundedness, to the global setting of $ L^p(\mathbb{R}^{n})$. Global boundedness in weighted Sobolev spaces $ W^{\sigma ,p}_s(\mathbb{R}^{n})$ is also established, and applications to hyperbolic partial differential equations are given.


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Additional Information

Sandro Coriasco
Affiliation: Dipartimento di Matematica “G. Peano”, Università di Torino, V. C. Alberto, n. 10, Torino I-10126, Italy
Email: sandro.coriasco@unito.it

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: m.ruzhansky@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05911-4
PII: S 0002-9947(2014)05911-4
Keywords: Fourier integral operators, global $L^p(\mathbb{R}^{n})$ boundedness
Received by editor(s): December 9, 2010
Received by editor(s) in revised form: July 9, 2012
Published electronically: January 13, 2014
Additional Notes: The second author was supported in part by the EPSRC grants EP/E062873/1 and EP/G007233/1.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.