Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
By Michael Ruzhansky, Mitsuru Sugimoto. 2003
86 citations recorded by the source corpus.
ABSTRACT The local L 2-mapping property of Fourier integral operators has been established in Hörmander (1971) and in Eskin (1970). In this article, we treat the global L 2-boundedness for a class of operators that appears naturally in many problems. As a consequence, we improve known global results for several classes of pseudodifferential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara (1978) or Kumano-go (1976). As an application, we show a global smoothing estimate for generalized Schrödinger equations which extends the results of Ben-Artzi and Devinatz (1991) and Walther (1999); (2002).
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3ef392d86702cf0d28b2617dd6538a6de27a4b99
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In Applied Mathematics
- Michael Ruzhansky
- Ville T. Turunen
- L. Rodino
- Sandro Coriasco
- Fabio Di Nicola
- Elena Cordero
- J. Delgado
- Niyaz Tokmagambetov
In Mathematical Physics
- Michael Ruzhansky
- Sandro Coriasco
- L. Rodino
- Ville T. Turunen
- Fabio Di Nicola
- Elena Cordero
- J. Delgado
- Niyaz Tokmagambetov
Citations in the corpus
- On the global boundedness of Fourier integral operators (2008, methodology): “Finally we observe that these results should extend to the more general class of global FIOs considered in [37]; we plan to devote a subsequent paper to this investigation.”
- Global $L^p$ continuity of Fourier integral operators (2009, methodology): “For example, it is shown in [26, 27] that for canonical transforms appearing there condition (2.”
- On the boundedness of Fourier integral operators on (2010, background): “On peut démontrer un résultat plus fort pour les opérateurs intégraux de Fourier étudiée dans [9] et [17] :”
- Quantization of Pseudo-differential Operators on the Torus (2008, result): “Therefore, this theorem relaxes assumptions on the behaviour with respect to the dual variable, compared, for example, with the corresponding result by Ruzhansky and Sugimoto [20].”