Product-type operators on weak vector valued α-Besov spaces

Abstract

$Let ψ_1 and ψ_2$ be analytic functions on the open unit disk mathbb{D} and φ an analytic self map on $mathbb{D}. Let M_ψ , C_φ and D$ denote the multiplication, composition and differentiation operators. We consider operators $M_{ψ1}C_φ , M_{ψ2}C_φD$ and the Stević-Sharma operator $T_{ψ1,ψ2,φ}(f) = M_{ψ1}C_φ(f)+M_{ψ2}C_φD(f)$ on α-Besov space Bp,α and weak vector valued α-Besov space wBp,α(X) for complex Banach space X and find some equivalent statements for boundedness of these operators. Also, boundedness and compactness of composition operator $C_φ on B_{p,α}(mathbb{D}) and _wB_{p,α}(mathbb{D})$ are given.