The paper shows the domination in M λ which is associated with the analytic Morrey space L 2,λ. We get the explicit expressions for upper bounds of Korenblum constants for the analytic Morrey space L 2,λ , the weighted Dirichlet space D p α , and the general function space F(p, q, s), etc. Furthermore, the domination in the Dirichlet space D α is investigated.