We present an elementary proof of two a priori estimates
for Schrödinger type multipliers on the circle. The first
is an $L^4 - L^2$ inequality of Bourgain, while the second is
a new $L^6 - L^{3/2}$ inequality. Estimates of this type are
useful for the study of the Cauchy problem for Schr\"odinger
type equations. The proofs are based on a counting argument
and standard real and harmonic analysis techniques.
Publié le : 2001-04-15
Classification:
42B15,
35B45,
35G25,
35J10,
35Q55
@article{1258138360,
author = {Himonas, A. Alexandrou and Misiolek, Gerard},
title = {A priori estimates for Schr\"odinger type multipliers},
journal = {Illinois J. Math.},
volume = {45},
number = {4},
year = {2001},
pages = { 631-640},
language = {en},
url = {http://dml.mathdoc.fr/item/1258138360}
}
Himonas, A. Alexandrou; Misiolek, Gerard. A priori estimates for Schrödinger type multipliers. Illinois J. Math., Tome 45 (2001) no. 4, pp. 631-640. http://gdmltest.u-ga.fr/item/1258138360/