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J. Korean Math. Soc. 2008; 45(4): 977-991

Printed July 1, 2008

Copyright © The Korean Mathematical Society.

Weighted composition operators from $F(p,q,s)$ into logarithmic Bloch space

Shanli Ye

Fujian Normal University

Abstract

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We characterize the boundedness and compactness of the weighted composition operator $uC_\varphi$ from the general function space $F(p$, $q$, $s)$ into the logarithmic Bloch space $\beta_L$ on the unit disk. Some necessary and sufficient conditions are given for which $uC_\varphi$ is a bounded or a compact operator from $F(p,q,s),\, F_0(p,q,s)$ into $\beta_L, \beta_L^0$ respectively.

Keywords: weighted composition operator, $F(p,q,s)$ space, logarithmic Bloch space

MSC numbers: Primary 47B38; Secondary 30H05

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