PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

doi:10.1007/s10473-024-0408-4

Abstract

Abstract: 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$T_{u,\psi,\varphi}f(z)=u(z)f(\varphi(z))+\psi(z)f'(\varphi(z)), \quad z\in\mathbb{D},$ acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

Key words: compactness, boundedness, Bloch type space, product type operator, weighted Bergman space

CLC Number:

47B33

Zuoling Liu, Hasi Wulan. PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES[J].Acta mathematica scientia,Series B, 2024, 44(4): 1327-1336.

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