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A note on a BMO map induced by strongly quasisymmetric homeomorphism


Authors: Yue Fan, Yun Hu and Yuliang Shen
Journal: Proc. Amer. Math. Soc. 145 (2017), 2505-2512
MSC (2010): Primary 30C62, 30F60, 32G15; Secondary 30H35
DOI: https://doi.org/10.1090/proc/13388
Published electronically: November 30, 2016
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Abstract: It is known that a sense preserving homeomorphism $ h$ of the unit circle induces a BMO map $ P_h$ by pull-back if and only if it is strongly quasisymmetric. In this note, we will discuss the compactness of the projection operator $ P^-_h$ sending a BMOA function $ \phi $ to the anti-holomorphic part of $ P_h\phi $.


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Additional Information

Yue Fan
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, People’s Republic of China
Email: 20144007001@stu.suda.edu.cn

Yun Hu
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, People’s Republic of China
Email: huyun_80@163.com

Yuliang Shen
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, People’s Republic of China
Email: ylshen@suda.edu.cn

DOI: https://doi.org/10.1090/proc/13388
Keywords: Strongly quasisymmetric homeomorphism, strongly symmetric homeomorphism, BMO, VMO, compact operator
Received by editor(s): June 16, 2016
Received by editor(s) in revised form: July 16, 2016
Published electronically: November 30, 2016
Additional Notes: This research was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2016 American Mathematical Society