An integral operator on $H\sp p$
To every analytic function $g$ in the unit disk $\bold D$ one associates the integral operator $T_g(f)(z)\coloneq z^{-1}\int^z_0f(\xi)g'(\xi)d\xi$ on spaces of analytic functions in $\bold D$. Operators of this form appear naturally in complex analysis. For instance, the choice $g(z)\equiv z$ leads to the integration operator, and the choice $g(z)=\log(1/(1-z))$ leads to the Cesàro operator. The