Publication at Faculty of Mathematics and Physics |
2010
Abstract
We prove that if f is integrable and approximately differentiable a.e., then the Hardy-Littlewood maximal function Mf is also approximately differentiable a.e. Moreover, if we only assume that f is integrable, 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 an integrable function on R such that Mf is not approximately differentiable a.e.