Essential norms of integral operators on spaces of analytic functions

This note aims at investigating the essential norms of integral operators on Banach spaces of analytic functions. We study the essential norm of _Ig$I_g$ on some classical Banach spaces (the Bloch space, BMOA$BMOA$ and the Dirichlet space). The essential norms of the Volterra type operator _Tg$T_g$ on the Bloch space are given by the distance from the logarithmic Bloch function to the little logarithmic Bloch space. The essential norms of the little Hankel operator are also investigated.