## Abstract

In this paper we investigate the behavior of the Hardy-Littlewood Maximal Operator. It is well known that for absolutely integrable functions the Hardy-Littlewood Maximal Operator is finite almost everywhere. In this paper it is shown that for each set E ⊂ [-π,π) with Lebesgue measure zero there exists a function of vanishing mean oscillation (VMO) such that the Hardy-Littlewood Maximal Operator of this function is infinite for all points of the set E. So for VMO-functions the Hardy-Littlewood Maximal Operator has divergence behavior similar to that of absolutely integrable functions. Some applications of these results for the behavior of the Poisson-Integral of VMO-functions are also given.

Original language | German |
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Pages (from-to) | 221-229 |

Number of pages | 9 |

Journal | Illinois Journal of Mathematics |

Volume | 44 |

Issue number | 2 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |