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arXiv · 1710.02033

On the pointwise domination of a function by its maximal function

J. M. Aldaz
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Abstract

We show that under rather general circumstances, the almost everywhere pointwise inequality $|f|(x) \le Mf (x)$ is equivalent to a weak form of the Lebesgue density theorem, for totally bounded closed sets. We derive both positive and negative results from this characterization.

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J. M. Aldaz. 2018-12-05. On the pointwise domination of a function by its maximal function. https://arxiv.org/abs/1710.02033

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