A description of $A_{\infty }$-weights for VMO
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- by Jinsong Liu, Fei Tao and Huaying Wei;
- Proc. Amer. Math. Soc. 151 (2023), 2997-3008
- DOI: https://doi.org/10.1090/proc/16345
- Published electronically: March 31, 2023
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Abstract:
We present a new characterization of Muckenhoupt $A_{\infty }$-weights whose logarithm is in vanishing mean oscillation $(\mathbb {R})$ in terms of vanishing Carleson measures on $\mathbb {R}_+^2$ and vanishing doubling weights on $\mathbb {R}$. This also gives a novel description of strongly symmetric homeomorphisms on the real line by using a geometric quantity.References
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Bibliographic Information
- Jinsong Liu
- Affiliation: HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
- MR Author ID: 692700
- Email: liujsong@math.ac.cn
- Fei Tao
- Affiliation: HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
- ORCID: 0000-0001-6369-5020
- Email: ferrytau@amss.ac.cn
- Huaying Wei
- Affiliation: Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, People’s Republic of China
- Email: hywei@jsnu.edu.cn
- Received by editor(s): August 8, 2022
- Received by editor(s) in revised form: October 12, 2022
- Published electronically: March 31, 2023
- Additional Notes: The first author was supported by National Key R$\&$D Program of China (Grant No. 2021YFA1003100), NSFC (Grant No. 11925107), Key Research Program of Frontier Sciences, CAS (Grant No. ZDBS-LY-7002); the third author was supported by the National Natural Science Foundation of China (Grant No. 12271218).
The second author is the correpsonding author. - Communicated by: Javad Mashreghi
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 2997-3008
- MSC (2020): Primary 30C62, 30H35; Secondary 26A46, 37E10
- DOI: https://doi.org/10.1090/proc/16345
- MathSciNet review: 4579373