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


Abstract: Let \varphi and \psi be holomorphic maps on D such that \varphi ( D ) \subset 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 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.

Keywords: Composition operator, Multiplication operator, Differentiation operator, Bergman space, Bloch space, Growth space

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