Best constants for uncentered maximal functions

Abstract

We precisely evaluate the operator norm of the uncentered Hardy-Littlewood maximal function on $L^p({\mathbb{R}}^1)$. We also compute the operator norm of the uncentered Hardy-Littlewood maximal function over rectangles on $L^p({\mathbb{R}}^n)$, and we show that the operator norm of the uncentered Hardy-Littlewood maximal function over balls on $L^p({\mathbb{R}}^n)$ grows exponentially with the dimension as $n\to \infty$.

Cited by in corpus (1)

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