On SteviĆ–Sharma operators from weighted Bergman spaces to weighted–type spaces

Let H (D) be the space of analytic functions on the unit disc D . Let ϕ be an analytic self-map of D and ψ1, ψ2 ∈ H (D) . Let C_ϕ , M_ψ and D denote the composition, multiplication and differentiation operators, respectively. In order to treat the products of these operators in a unified manner, Stević et al. introduced the following operator T_ψ1 ,ψ2 ,_ϕ f = ψ1 · f ◦ ϕ + ψ2 · f ◦ ϕ, f ∈ H (D). We characterize the boundedness and compactness of the operators T_ψ1 ,ψ2 ,_ϕ from weighted Bergman spaces to weighted-type and little weighted-type spaces of analytic functions. Also, we give examples of bounded, unbounded, compact and non compact operators T_ψ1 ,ψ2 ,ϕ .