Given a rotation invariant measure in $\Bbb R^n$, we define the maximal operator over circular sectors. We prove that it is of strong type $(p,p)$ for $p>1$ and we give necessary and sufficient conditions on the measure for the weak type $(1,1)$ inequality. Actually we work in a more general setting containing the above and other situations.
@article{119245,
author = {Hugo A. Aimar and Liliana Forzani and Virginia Naibo},
title = {On maximal functions over circular sectors with rotation invariant measures},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {42},
year = {2001},
pages = {311-318},
zbl = {1054.42014},
mrnumber = {1832149},
language = {en},
url = {http://dml.mathdoc.fr/item/119245}
}
Aimar, Hugo A.; Forzani, Liliana; Naibo, Virginia. On maximal functions over circular sectors with rotation invariant measures. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 311-318. http://gdmltest.u-ga.fr/item/119245/
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