Weak compactness and essential norms of integration operators

Abstract

Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_{g}f(z)={\int }_0^{z}f{g}^{\prime }d\zeta$. We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is compact. In the case of $BMOA$ this answers a question of Siskakis and Zhao. More generally, we estimate the essential and weak essential norms of $T_g$ on $H^p$ and $BMOA$.

References in corpus (1)

• Compact and weakly compact composition operators on BMOA