Abstract

Let $H(\Bbb D)$ denote the space of all analytic functions on the unit disk $\Bbb D$ of $\Bbb C$. In this paper we consider the following Volterra type operator $$J_g(f)(z)=\int_0^zf(\xi)g'(\xi)\,d\xi,\quad f\in H(\Bbb D),\; z\in\Bbb D.$$ The boundedness and compactness of the operator $J_g$ from the weighted Hardy space to a Bloch space are studied.

Keywords: Volterra type operator; weighted Hardy space; Bloch space; boundedness; compactness.

MSC: 47B38, 32A18

Pages:  481$-$487     

Volume  65 ,  Issue  4 ,  2013