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Product type operators acting between weighted Bergman spaces and Bloch type spaces

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Abstract

For analytic functions u, ψ in the unit disk ⅅ in the complex plane and an analytic self-map φ of 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.

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, China

    Zuoling Liu & Hasi Wulan

Authors
  1. Zuoling Liu
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  2. Hasi Wulan
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Correspondence to Hasi Wulan.

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Conflict of Interest The authors declare that they have no conflict of interest.

Additional information

The work was supported by the NSFC (11720101003, 12071272).

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Liu, Z., Wulan, H. Product type operators acting between weighted Bergman spaces and Bloch type spaces. Acta Math Sci 44, 1327–1336 (2024). https://doi.org/10.1007/s10473-024-0408-4

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  • DOI: https://doi.org/10.1007/s10473-024-0408-4

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