Bull. Korean Math. Soc. 2010; 47(3): 527-540
Printed May 1, 2010
https://doi.org/10.4134/BKMS.2010.47.3.527
Copyright © The Korean Mathematical Society.
Shanli Ye
Fujian Normal University
We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal L\mathcal B=\{f\in H(D):\sup_D (1-|z|^2)\ln(\frac{2}{1-|z|})|f'(z)|<+\infty\}$ and the little logarithmic Bloch space $\mathcal L\mathcal B_o$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space $\mathcal L\mathcal B$ and the little logarithmic Bloch space $\mathcal L\mathcal B_o$.
Keywords: logarithmic Bloch space, weighted composition operator, boundedness, compactness
MSC numbers: 47B38, 30D05, 30H05
2023; 60(4): 957-969
2020; 57(3): 583-595
2015; 52(4): 1383-1399
2019; 56(4): 885-898
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd