On approximate differentiability of the maximal function

By P. Hajłasz, Jan Maly. 2010

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We prove that if f ∈ L 1 (ℝ n ) is approximately differentiable a.e., then the Hardy-Littlewood maximal function Mf is also approximately differentiable a.e. Moreover, if we only assume that f ∈ L 1 (ℝ n ), then any open set of ℝ n contains a subset of positive measure such that Mf is approximately differentiable on that set. On the other hand we present an example of f ∈ L 1 (ℝ) such that Mf is not approximately differentiable a.e.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/89cd7df86f73a4af9c8592c1e7ac8a19b2fadcae