H. Aimar, L. Forzani, V. Naibo
On maximal functions over circular sectors with rotation invariant measures

Comment.Math.Univ.Carolinae 42,2 (2001) 311-318.

Abstract: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.

Keywords: maximal functions, spaces of homogeneous type
AMS Subject Classification: 42B25