| 林庆泽.关于Cordoba-Fefferman覆盖性质的一个等价刻画[J].海南师范大学学报自科版,2021,34(2):119-123 |
| 关于Cordoba-Fefferman覆盖性质的一个等价刻画 |
| An Equivalent Characterization ofCordoba-Fefferman Covering Property |
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| DOI：10.12051/j.issn.1674-4942.2021.02.001 |
| 中文关键词: 覆盖性质 强极大定理 有限覆盖性质 有界性 |
| 英文关键词: covering property strong maximal theorem finite covering property boundedness |
| 基金项目:国家自然科学基金项目（11801094） |
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| 摘要点击次数: 548 |
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| 中文摘要: |
| 本研究通过证明强极大算子的有界性得到Rn上具有有界Lebesgue测度的开集族具有
Cordoba-Fefferman覆盖性质与它具有有限覆盖性质的等价性，最后给出两个推论：（1）给定由Rn上
某些具有有界Lebesgue测度的开集所组成的族ℑ，则族ℑ不仅具有有限覆盖性质W1，而且也具有覆
盖性质V1；（2）Rn
上所有边平行于坐标轴的n维矩形所组成的集族不仅具有有限覆盖性质Wq，同时
也具有覆盖性质Vq，其中1 ≤ q < ∞。 |
| 英文摘要: |
| In this paper, by proving the boundedness of the strongly maximal operators, the equivalence between the Cor⁃
doba-Fefferman covering property and the finite covering property of open sets with bounded Lebesgue measures on
Rnwere obtained. Finally, two corollaries were given: (1) Given the family ℑ of some open sets with bounded Lebesgue mea⁃
sures in Rn, the ℑ has not only the finite covering property W1, but also the covering property V1; (2) The family of all n-di⁃
mensional rectangles with sides parallel to coordinate axes in Rn has not only the finite covering property Wq, but also the
covering property Vq, where 1 ≤ q < ∞. |
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