# A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE

• Ye, Shanli (Department of Mathematics Fujian Normal University)
• Published : 2010.05.31
• 111 15

#### Abstract

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

#### Keywords

logarithmic Bloch space;weighted composition operator;boundedness;compactness

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