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Weighted Sobolev L 2 estimates for a class of Fourier integral operators
Author(s) -
Ruzhansky Michael,
Sugimoto Mitsuru
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910080
Subject(s) - mathematics , sobolev space , fourier transform , fourier integral operator , smoothing , class (philosophy) , fourier analysis , microlocal analysis , mathematical analysis , partial differential equation , space (punctuation) , type (biology) , pure mathematics , integral equation , statistics , artificial intelligence , computer science , ecology , linguistics , philosophy , biology
In this paper we develop elements of the global calculus of Fourier integral operators in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathbb R}^n}$\end{document} under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L 2 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.