Fixed points of the uncentered Hardy-Littlewood maximal operator

Wu-Yi Pan

Fixed points of the uncentered Hardy-Littlewood maximal operator

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arxiv 2211.15147 v1 pith:SSBVF7P3 submitted 2022-11-28 math.MG

Wu-yi Pan This is my paper

classification math.MG

keywords fixedpointsmaximalmeasureoperatoruncenteredassumptionbeingness

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We give a survey, known and new results on the beingness of fixed points of the maximal operator in the more general settings of metric measure space. In particular, we prove that the fixed points of the uncentered one must be the constant function if the measure satisfies a mild continuity assumption and its support is connected.

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