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In this paper, we establish a Bloch-type growth theorem for generalizedBloch-type spaces and discuss relationships between Dirichlet-type spaces andHardy-type spaces on certain classes of complex-valued functions. Then wepresent some applications to non-homogeneous Yukawa PDEs. We also consider someproperties of the Lipschitz-type spaces on certain classes of complex-valuedfunctions. Finally, we will study a class of composition operators on thesespaces.

On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces