We prove that the elliptic maximal function maps the Sobolev space
$W_{4,\eta}(\mathbb{R}^2)$ into $L^4(\mathbb{R}^2)$ for all $\eta>1/6$.
The main ingredients of the proof are an analysis of the intersection properties
of elliptic annuli and a combinatorial method of Kolasa and Wolff.
Publié le : 2003-03-15
Classification:
Multiparameter maximal functions,
circular maximal function,
Sobolev space estimates,
42B25
@article{1049123086,
author = {Erdo\u gan, Mehmet Burak},
title = {Mapping properties of the elliptic maximal function},
journal = {Rev. Mat. Iberoamericana},
volume = {19},
number = {2},
year = {2003},
pages = { 221-234},
language = {en},
url = {http://dml.mathdoc.fr/item/1049123086}
}
Erdoğan, Mehmet Burak. Mapping properties of the elliptic maximal function. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp. 221-234. http://gdmltest.u-ga.fr/item/1049123086/