Weighted differentiation composition operator from logarithmic Bloch spaces to Zygmund-type spaces
Summary: Let \(H(\mathbb{D})\) denote the space of all holomorphic functions on the unit disk \(\mathbb{D}\) of \(\mathbb C\), \(u \in H(\mathbb{D})\) and let \(n\) be a positive integer, \(\varphi\) a holomorphic self-map of \(\mathbb{D}\), and \(\mu\) a weight. In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator \(\mathcal{D}_{\varphi, u}^n f(z) = u(z) f^{(n)}(\varphi(z))\), \(f \in H(\mathbb{D})\), from the logarithmic Bloch spaces to the Zygmund-type spaces.
weighted differentiation composition operator
scientific article; zbMATH DE number 7023157
scientific article