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- W2057996843 abstract "We prove that if $fin L^1(mathbb {R}^n)$ is approximately differentiable a.e., then the Hardy-Littlewood maximal function $mathcal {M}f$ is also approximately differentiable a.e. Moreover, if we only assume that $fin L^1(mathbb {R}^n)$, then any open set of $mathbb {R}^n$ contains a subset of positive measure such that $mathcal {M} f$ is approximately differentiable on that set. On the other hand we present an example of $fin L^1(mathbb {R})$ such that $mathcal {M}f$ is not approximately differentiable a.e." @default.
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- W2057996843 date "2010-01-01" @default.
- W2057996843 modified "2023-10-14" @default.
- W2057996843 title "On approximate differentiability of the maximal function" @default.
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- W2057996843 doi "https://doi.org/10.1090/s0002-9939-09-09971-7" @default.
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