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arXiv · 2107.12404

The one-dimensional centred maximal function diminishes the variation of indicator functions

Constantin Bilz·Julian Weigt
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Abstract

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results to a larger class of functions.

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Constantin Bilz, Julian Weigt. 2021-07-26. The one-dimensional centred maximal function diminishes the variation of indicator functions. https://arxiv.org/abs/2107.12404

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