Volterra composition operators on logarithmic Bloch spaces

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.