For cylindrically symmetric functions dyadically supported on the
paraboloid, we obtain a family of sharp linear and bilinear adjoint
restriction estimates. As corollaries, we first extend the ranges of
exponents for the classical \textit{linear or bilinear adjoint
restriction conjectures} for such functions and verify the
\textit{linear adjoint restriction conjecture} for the paraboloid.
We also interpret the restriction estimates in terms of solutions to
the Schrödinger equation and establish the analogous results when
the paraboloid is replaced by the lower third of the sphere.
@article{1257258103,
author = {Shao
,
Shuanglin},
title = {Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case},
journal = {Rev. Mat. Iberoamericana},
volume = {25},
number = {1},
year = {2009},
pages = { 1127-1168},
language = {en},
url = {http://dml.mathdoc.fr/item/1257258103}
}
Shao
,
Shuanglin. Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case. Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, pp. 1127-1168. http://gdmltest.u-ga.fr/item/1257258103/