Strongly continuous composition semigroups on analytic Morrey spaces

For a semigroup (phi(t)t >= 0) consisting of analytic self-maps from the unit disk D to itself, a strongly continuous composition semi-group (C-t)t >= 0 induced by (phi(t))(t >= 0) on analytic Morrey spaces H-2,H-lambda, 0 < lambda < 1, is investigated. By the weak compactness of resolvent operator, we give a complete characterization of H-0(2,lambda )= [phi(t), H-2,H-lambda] for 0 < lambda < 1 in terms of the infinitesimal generator if the Denjoy-Wolff point of (phi(t))(t >= 0) is in D.