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

doi:10.1007/s10473-023-0103-x

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 43-50.doi: 10.1007/s10473-023-0103-x

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

Shanli YE, Zhihui ZHOU

School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

收稿日期:2021-10-29 修回日期:2022-06-28 发布日期:2023-03-01
基金资助:
*National Natural Science Foundation of China (11671357, 11801508).

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

Shanli YE, Zhihui ZHOU

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).

摘要/Abstract

摘要： 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 $\alpha\in\mathbb{R}$.

关键词: closure, logarithmic Bloch spaces, BMOA

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

Shanli YE, Zhihui ZHOU. CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES^*[J]. 数学物理学报(英文版), 2023, 43(1): 43-50.

Shanli YE, Zhihui ZHOU. CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 43-50.

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

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

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