Carleson Measure Characterization of Weighted BMO Associated with a Family of General Sets

详细信息    查看全文

• 作者：Yong Ding ; Ming-Yi Lee ; Chin-Cheng Lin
• 关键词：\(A_p\) ; weights ; BMO ; Carleson measure ; Calderón–Zygmund operator ; Hardy spaces ; Maximal operator
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：842-867
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

In this paper, we introduce a weighted Carleson measure \(d\nu _{\mathbb {E}, w}\) associated with the family \(\mathbb {E}\), where \(\mathbb {E}=\{E_r(x)\}_{r\in \mathcal {I}, x\in X}\) is a family of open subsets of a topological space X endowed with a nonnegative Borel measure \(\mu \) satisfying certain basic conditions. Using Calderón–Zygmund theory, we show that the weighted BMO associated with the family \(\mathbb {E}\) can be characterized by the weighted Carleson measure \(d\nu _{\mathbb {E}, w}\).