### 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 $\alpha\in\mathbb{R}$, the logarithmic Bloch space $\mathscr{B}_{L^{\alpha}}$ consists of those functions $f$ which are analytic in the unit disk $\mathbb{D}$ with $\sup_{z\in\mathbb{D}}(1-|z|^2)\left(\log\frac{\rm e}{1-|z|^2}\right)^{\alpha}|f'(z)|<\infty.$ In this paper, we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space $\mathscr{B}_{L^{\alpha}}$ for all $\alpha\in\mathbb{R}$.

Key words: closure, logarithmic Bloch spaces, BMOA

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