## 摘要

Let VMO_{F} denote the closure of C_{c}∩Lip with respect to the seminorm ‖⋅‖_{BMOF}, where F is a family of sections and the space BMO_{F} associated to the family F was introduced by Caffarelli and Gutiérrez (1996) [4]. Sections play an important role in the investigation of Monge–Ampère equation and the linearized Monge–Ampère equation. We show that the dual of VMO_{F} is the Hardy space H_{F} ^{1} defined in Ding and Lin (2005) [8]. As an application, we prove that μ-almost everywhere convergence of a sequence of functions bounded in H_{F} ^{1} to a function in L^{1}(dμ) implies the weak* convergence.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 463-476 |

頁數 | 14 |

期刊 | Journal of Mathematical Analysis and Applications |

卷 | 455 |

發行號 | 1 |

DOIs | |

出版狀態 | 已出版 - 1 11月 2017 |

## 指紋

深入研究「On the weak* convergence in H_{F}

^{1}(R

^{n})」主題。共同形成了獨特的指紋。