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Generalized weighted composition operators on Bergman spaces induced by doubling weights by Liu, Bin is a scholarly article available to read on EtoBox.

What is Generalized weighted composition operators on Bergman spaces induced by doubling weights about?

Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling condition, to a Lebesgue space $L^q_\nu$ are characterized. On the way to the proofs a new embedding theorem on weighted Bergman spaces $A^p_\omega$ is established. This last-mentioned result generalizes the well-known characterization of the boundedness of the differentiation operator $D^n(f)=f^{(n)}$ from the classical weighted Bergman space $A^p_\alpha$ to the Lebesgue space $L^q_\mu$, induced by a positive Borel measure $\mu$, to the setting of doubling weights.

Author

Liu, Bin

Published

2020

Language

EN