A weighted composition operator on the logarithmic Bloch space
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 527-540
https://doi.org/10.4134/BKMS.2010.47.3.527
Published online May 1, 2010
Shanli Ye
Fujian Normal University
Abstract : 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
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