Norm-attaining integral operators on analytic function spaces

If f and g are analytic functions in the unit disc D we define S g ( f ) ( z ) = ∫ 0 z f ′ ( w ) g ( w ) d w , ( z ∈ D ) . If g is bounded then the integral operator S g is bounded on the Bloch space, on the Dirichlet space, and on B M O A . We show that S g is norm-attaining on the Bloch space and on B M O A for any bounded analytic function g , but does not attain its norm on the Dirichlet space for non-constant g . Some results are also obtained for S g on the little Bloch space, and for another integral operator T g from the Dirichlet space to the Bergman space.