Volterra composition operators on logarithmic Bloch spaces
Xiangling Zhu
Source: Banach J. Math. Anal. Volume 3, Number 1 (2009), 122-130.
Abstract
Let $\varphi$ be a holomorphic self-map and $g$ a fixed holomorphic function on the unit ball $B$. The boundedness and compactness of the Volterra composition operator $$T_{g,\varphi} f(z)= \int_0^1 f(\varphi(tz)) \Re g(tz)\frac{dt}{t}$$ on the logarithmic Bloch space and little logarithmic Bloch space are studied in this paper.
Primary Subjects: 47B38
Secondary Subjects: 32A37
Keywords: Volterra composition operator; logarithmic Bloch space; Bloch space
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Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336429
Mathematical Reviews number (MathSciNet):
MR2461752
Zentralblatt MATH identifier:
1163.47022
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