%A Shanli YE, Zhihui ZHOU %T CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES* %0 Journal Article %D 2023 %J Acta mathematica scientia,Series B %R 10.1007/s10473-023-0103-x %P 43-50 %V 43 %N 1 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16905.shtml} %8 2023-02-25 %X 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 $\alpha\in\mathbb{R}$.