Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (1): 43-50.doi: 10.1007/s10473-023-0103-x

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CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES*

Shanli YE, Zhihui ZHOU   

  1. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
  • Received:2021-10-29 Revised:2022-06-28 Published:2023-03-01
  • About author:Shanli YE, E-mail: slye@zust.edu.cn; Zhihui ZHOU, zzhh144@163.com
  • Supported by:
    *National Natural Science Foundation of China (11671357, 11801508).

Abstract: For any αR, the logarithmic Bloch space BLα consists of those functions f which are analytic in the unit disk D with supzD(1|z|2)(loge1|z|2)α|f(z)|<. In this paper, we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLα for all αR.

Key words: closure, logarithmic Bloch spaces, BMOA

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