### On maximal functions over circular sectors with rotation invariant measures

Given a rotation invariant measure in ${\mathbb{R}}^{n}$, 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.