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Weighted Sobolev L2 estimates for a class of Fourier integral operators

✍ Scribed by Michael Ruzhansky; Mitsuru Sugimoto

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
235 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

In this paper we develop elements of the global calculus of Fourier integral operators in R n 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.

πŸ“œ SIMILAR VOLUMES

Weighted Lp Inequalities for a Class of
Weighted Lp Inequalities for a Class of Integral Operators Including the Classical Index Transforms
✍ Benito J. GonzΓ‘lez; Emilio R. Negrin πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 74 KB

In this paper we study the behaviour of certain integral operators acting on weighted L p spaces. Particular cases include the classical integral transforms of Kontorovich and Lebedev and Mehler and Fock and the F -index transform 2 1 considered by Gonzalez, Hayek, and Negrin.