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Closure of Analytic Functions of the Bounded Mean Oscillation in Logarithmic Bloch Spaces

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Abstract

For any α ∈ ℝ, the logarithmic Bloch space \({{\cal B}_{{L^\alpha}}}\) consists of those functions f which are analytic in the unit disk ⅅ with

$$\mathop {\sup }\limits_{z \in \mathbb{D}} (1 - {\left| z \right|^2}){\left( {\log \frac{e}{{1 - {{\left| z \right|}^2}}}} \right)^\alpha }\left| {f'(z)} \right| < \infty .$$

In this paper, we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space \({{\cal B}_{{L^\alpha}}}\) for all α ∈ ℝ.

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Authors and Affiliations

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

    Shanli Ye & Zhihui Zhou

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  1. Shanli Ye
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  2. Zhihui Zhou
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Correspondence to Shanli Ye or Zhihui Zhou.

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The research was supported by the National Natural Science Foundation of China (11671357, 11801508).

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Ye, S., Zhou, Z. Closure of Analytic Functions of the Bounded Mean Oscillation in Logarithmic Bloch Spaces. Acta Math Sci 43, 43–50 (2023). https://doi.org/10.1007/s10473-023-0103-x

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  • DOI: https://doi.org/10.1007/s10473-023-0103-x

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