On Stević-Sharma operators from weighted Bergman spaces to weighted-type spaces

Abstract

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 Cφ , Mψ 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 Tψ1 ,ψ2 ,φ f = ψ1 · f ◦φ +ψ2 · f ′ ◦φ , f ∈ H (D). We characterize the boundedness and compactness of the operators Tψ1 ,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 Tψ1 ,ψ2 ,φ . Mathematics subject classification (2010): 47B33, 47B38.