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Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan GreenleafGunther Uhlmann — 1990

Annales de l'institut Fourier

We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ( T * X 0 ) × ( T * Y 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C T * Y is a Whitney fold and ρ : C T * X is a blow-down mapping. If A I m ( C ) , B I m ' ( C t ) , then B A I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

Oscillatory and Fourier integral operators with degenerate canonical relations.

Allan GreenleafAndreas Seeger — 2002

Publicacions Matemàtiques

We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

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