# About regularity of the maximal operator of Hardy-Littlewood

What difficulties arise when you consider the centered maximal operator, such that you can't prove that it maps BV into BV?

Does someone have some reference which that maps BV into BV?

PS: The non-centered operator maps BV into BV, correct me if I am wrong, but for the centered maximal operators it remains an open problem!

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I'm not sure what the second question means, can you rephrase it? –  Chris Janjigian May 2 '12 at 22:56
You get a bit more for the non-centred operator: it maps BV into AC (it is actually regularity improving). –  Willie Wong May 3 '12 at 8:45
The article is not available for non-registered users. –  checkmath May 3 '12 at 17:03
Try this arXiv.org link. –  robjohn May 4 '12 at 15:00