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arXiv · 1807.04399

Centered Hardy--Littlewood maximal operator on the real line: lower bounds

Paata Ivanisvili·Samuel Zbarsky
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Abstract

For $1 0$ such that $\|Mf\|_p\ge (1+\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\le p<\infty$, we prove the inequality for indicator functions and for unimodal functions.

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Paata Ivanisvili, Samuel Zbarsky. 2018-07-12. Centered Hardy--Littlewood maximal operator on the real line: lower bounds. https://doi.org/10.1016/j.crma.2019.03.003

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