On a product-type operator from weighted Bergman-Orlicz space to some weighted type spaces

Let D={z∈C:|z|<1} be the open unit disk, φ an analytic self-map of D and ψ an analytic function on D. Let D be the differentiation operator and Wφ,ψ the weighted composition operator. The boundedness and compactness of the product-type operator DWφ,ψ from the weighted Bergman-Orlicz space to the Bers type space, weighted Bloch space and weighted Zygmund space on D are characterized.