## Abstract

In this paper we prove a discrete version of Tanaka's theorem for the Hardy-Littlewood maximal operator in dimension , both in the non-centered and centered cases. For the non-centered maximal operator we prove that, given a function of bounded variation,

where represents the total variation of . For the centered maximal operator we prove that, given a function such that ,

This provides a positive solution to a question of Hajłasz and Onninen in the discrete one-dimensional case.

where represents the total variation of . For the centered maximal operator we prove that, given a function such that ,

This provides a positive solution to a question of Hajłasz and Onninen in the discrete one-dimensional case.

Original language | English |
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Pages (from-to) | 1669-1680 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 |