Poincaré inequalities for the maximal function

Published 17 May 2016 in math.CA | (1605.05176v2)

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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Olli Saari

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