Weighted Sobolev L2 estimates for a class of Fourier integral operators |
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Authors: | Michael Ruzhansky Mitsuru Sugimoto |
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Institution: | 1. Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK;2. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464‐8602, Japan |
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Abstract: | In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions. |
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Keywords: | Fourier integral operators pseudo‐differential operators weighted estimates Sobolev spaces smoothing estimates MSC (2010) 35S30 47G30 35J10 35G10 35B65 |
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