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arXiv · 1605.05176

Poincar\'e inequalities for the maximal function

Olli Saari
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Abstract

We study generalized Poincar\'e inequalities. We prove that if a function satisfies a suitable inequality of Poincar\'e 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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BibTeXRIS

Olli Saari. 2016-05-17. Poincar\'e inequalities for the maximal function. https://doi.org/10.2422/2036-2145.201705_001

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