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On maximal functions over circular sectors with rotation invariant measures

Hugo A. Aimar; Liliana Forzani; Virginia Naibo — 2001

Commentationes Mathematicae Universitatis Carolinae

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

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