We prove sharp $L\sp 2$-estimates for oscillatory integral and
Fourier integral operators for which the associated canonical relation
$\mathscr {C}\subset T\sp \ast\Omega\sb L\times T\sp \ast\Omega\sb R$
projects to $T\sp \ast\Omega\sb L$ and to $T\sp \ast\Omega\sb R$ with
corank 1 singularities of type $\leq 2$. This includes two-sided cusp
singularities. Applications are given to operators with one-sided
swallowtail singularities such as restricted X-ray transforms for
well-curved line complexes in five dimensions.
Publié le : 2002-04-15
Classification:
35S30,
42B20,
47G10,
58J40
@article{1087575182,
author = {Greenleaf, Allan and Seeger, Andreas},
title = {Oscillatory integral operators with low-order degeneracies},
journal = {Duke Math. J.},
volume = {115},
number = {1},
year = {2002},
pages = { 397-420},
language = {en},
url = {http://dml.mathdoc.fr/item/1087575182}
}
Greenleaf, Allan; Seeger, Andreas. Oscillatory integral operators with low-order degeneracies. Duke Math. J., Tome 115 (2002) no. 1, pp. 397-420. http://gdmltest.u-ga.fr/item/1087575182/