Product type operators acting between weighted Bergman spaces and Bloch type spaces. (English) Zbl 07844462
Summary: For analytic functions \(u\), \(\psi\) in the unit disk \(\mathbb{D}\) in the complex plane and an analytic self-map \(\varphi\) of \(\mathbb{D}\), we describe in this paper the boundedness and compactness of product type operators
\[
T_{u, \psi, \varphi}f(z) = u(z)f(\varphi(z)) + \psi(z)f^\prime(\varphi(z)), \quad z\in\mathbb{D},
\]
acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
MSC:
| 47B33 | Linear composition operators |
| 47B91 | Operators on complex function spaces |
| 30H20 | Bergman spaces and Fock spaces |
| 30H10 | Hardy spaces |
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