Abstract
We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space LB = {f 2 H(D) : supD(1 i |z| 2 )ln( 2 1i|z| )|f 0 (z)| < +1} and the little loga- rithmic Bloch space LB0. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space LB and the little logarithmic Bloch space LB0.
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