Integration and differentiation operators between growth spaces

For arbitrary radial weights $w$ and $u$, we study the integration operator between the growth spaces $H_w^{\mathrm{\infty }}$ and $H_u^{\mathrm{\infty }}$ on the complex plane. Also, we investigate the differentiation operator on the Hardy growth spaces $H_w^p$, $0<p<\mathrm{\infty }$, defined on the unit disk or on the complex plane. As in the case $p=\mathrm{\infty }$, the log-convex weights $w$ play a special role in the problems under consideration.