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Abstract: If and are analytic functions in the unit disc we define . If is bounded then the integral operator is bounded on the Bloch space, on the Dirichlet space, and on . We show that is norm-attaining on the Bloch space and on for any bounded analytic function , but does not attain its norm on the Dirichlet space for non-constant . Some results are also obtained for on the little Bloch space, and for another integral operator from the Dirichlet space to the Bergman space. [Copyright &y& Elsevier]

Abstract: This note aims at investigating the essential norms of integral operators on Banach spaces of analytic functions. We study the essential norm of Ig on some classical Banach spaces (the Bloch space, BMOA and the Dirichlet space). The essential norms of the Volterra type operator Tg 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. [Copyright &y& Elsevier]