Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces

Abstract

Let $varphi$ and $psi$ be holomorphic maps on $Bbb{D}$ such that $varphi(Bbb{D}) subset Bbb{D}$. Let $C_{varphi},M_{varphi}$ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces $A^{beta}_{N}$ to Bloch-type spaces. In fact, we prove that these operators map $A^{beta}_{N}$ compactly into Bloch-type spaces if and only if they map $A^{beta}_{N}$ boundedly into these spaces.