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Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces. (English) Zbl 1236.47025
Summary: Let $\varphi$ and $\psi$ be holomorphic maps on $\Bbb D$ such that $\varphi(\Bbb D) \subset \Bbb D$. Let $C_{\varphi}$, $M_{\psi}$ 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 $\cal A^{\beta}_{\cal N}$ to Bloch-type spaces. In fact, we prove that these operators map $\cal A^{\beta}_{\cal N}$ compactly into Bloch-type spaces if and only if they map $\cal A^{\beta}_{\cal N}$ boundedly into these spaces.

47B38Operators on function spaces (general)
47B33Composition operators
46E10Topological linear spaces of continuous, differentiable or analytic functions
30H10Hardy spaces
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