Abstract
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 \(d\nu _{\mathbb {E}, w}\).
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Acknowledgments
The authors would like to express their gratitude to the referee for his/her very careful reading, important comments and valuable suggestions. The authors are also indebted to the referee for drawing the helpful Ref. [3] to their attention. The first author was supported by NSFC (Nos. 11371057, 11471033, 11571160), the Fundamental Research Funds for the Central Universities (No. 2014KJJCA10) and SRFDP (No. 20130003110003). The second and third authors were supported by Ministry of Science and Technology of Taiwan under Grant #MOST 104-2115-M-008-002-MY2 and Grant #MOST 103-2115-M-008-003-MY3, respectively, as well as supported by National Center for Theoretical Sciences of Taiwan.
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Ding, Y., Lee, MY. & Lin, CC. Carleson Measure Characterization of Weighted BMO Associated with a Family of General Sets. J Geom Anal 27, 842–867 (2017). https://doi.org/10.1007/s12220-016-9700-4
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DOI: https://doi.org/10.1007/s12220-016-9700-4