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 $\alpha\in\mathbb{R}$.
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
.
DOI: 10.1007/s10473-023-0103-x
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