We study Fourier integral operators of Hörmander’s type acting on the spaces , 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in . We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on if the mapping is constant on the fibres, of codimension r, of an affine fibration.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-3-1,
author = {Fabio Nicola},
title = {Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {207-219},
zbl = {1192.35196},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-3-1}
}
Fabio Nicola. Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations. Studia Mathematica, Tome 196 (2010) pp. 207-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-3-1/