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arXiv · 1605.05176

Poincaré inequalities for the maximal function

Olli Saari
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Abstract

We study generalized Poincaré inequalities. We prove that if a function satisfies a suitable inequality of Poincaré type, then the Hardy-Littlewood maximal function also obeys a meaningful estimate of similar form. As a by-product, we get a unified approach to proving that the maximal operator is bounded on Sobolev, Lipschitz and BMO spaces.

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Olli Saari. 2017-02-16. Poincaré inequalities for the maximal function. https://doi.org/10.2422/2036-2145.201705_001

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