We investigate the $L^2$ boundedness of the triple Hilbert transform
along the surface given by the graph of a real polynomial $P$ of
three variables. We are interested in understanding the relationship
between the geometric properties of the Newton polyhedron of $P$ and
the analytic property of $L^2$ boundedness.
Publié le : 2009-06-15
Classification:
Hilbert transform,
Newton polyhedron,
oscillatory integrals,
42B15
@article{1255440065,
author = {Carbery
,
Anthony and Wainger
,
Stephen and Wright
,
James},
title = {Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$},
journal = {Rev. Mat. Iberoamericana},
volume = {25},
number = {1},
year = {2009},
pages = { 471-519},
language = {en},
url = {http://dml.mathdoc.fr/item/1255440065}
}
Carbery
,
Anthony; Wainger
,
Stephen; Wright
,
James. Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$. Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, pp. 471-519. http://gdmltest.u-ga.fr/item/1255440065/