Compactness of Composition Operators from the Bloch Space . to Q K Spaces

Suppose that . is an analytic self-map of the unit disk .. We consider compactness of the composition operator C . from the Bloch space . into the spaces Q K defined by a nonnegative, nondecreasing function K(r) for 0 . r < .. Our compactness condition depends only on . which can be considered as a slight improvement of the known results. The compactness of C . from the Dirichlet space D into the spaces Q K is also investigated.