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On maximal functions over circular sectors with rotation invariant measures

Hugo A. AimarLiliana ForzaniVirginia Naibo — 2001

Commentationes Mathematicae Universitatis Carolinae

Given a rotation invariant measure in 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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