Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms
Annales de l'Institut Fourier, Volume 40 (1990) no. 2, p. 443-466
We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C(T * X0)×(T * Y0). These canonical relations, which arise naturally in integral geometry, are such that π : CT * Y is a Whitney fold and ρ : CT * X is a blow-down mapping. If AI m (C), BI m (C t ), then BAI 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.
Nous établissons un calcul de composition pour les opérateurs intégraux de Fourier associés à une classe de relations canoniques lisses C(T * X0)×(T * Y0). Ces relations canoniques, qui se présentent en géométrie intégrale sont telles que π : CT * Y est un pli de Whitney et ρ : CT * X est une application blow-down. Si AI m (C), BI m (C t ), alors BAI m+m ,0 (Δ,Λ) qui est une classe d’opérateurs pseudodifférentiels avec des symboles singuliers. Il s’ensuit que A est borné sur L 2 avec une perte de dérivée d’un 1/4.
@article{AIF_1990__40_2_443_0,
     author = {Greenleaf, Allan and Uhlmann, Gunther},
     title = {Composition of some singular Fourier integral operators and estimates for restricted $X$-ray transforms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {40},
     number = {2},
     year = {1990},
     pages = {443-466},
     doi = {10.5802/aif.1220},
     zbl = {0695.58026},
     mrnumber = {91k:58126},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1990__40_2_443_0}
}
Greenleaf, Allan; Uhlmann, Gunther. Composition of some singular Fourier integral operators and estimates for restricted $X$-ray transforms. Annales de l'Institut Fourier, Volume 40 (1990) no. 2, pp. 443-466. doi : 10.5802/aif.1220. http://www.numdam.org/item/AIF_1990__40_2_443_0/

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