Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

A weighted composition operator on the logarithmic Bloch space

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