A note on weighted Bergman spaces and the Cesàro operator.(English)Zbl 0981.32001

Let $$A^p(dV_{\alpha})$$ denote the set of the functions holomorphic in the unit ball in $$\mathbb{C}^n$$, which belong to $$L^p(dV_{\alpha})$$ where $$\alpha >-1$$, $$0<p<\infty$$ and $$dV_{\alpha}={(1-|z|^2)}^{\alpha} dV(z)$$. In this paper $$A^p(dV_{\alpha})$$ is characterized as those functions whose images under the action of a certain set of differential operators lie in $$L^p(dV_{\alpha})$$. It is shown also that the Cesàro operator is bounded on $$A^p(dV_{\alpha})$$.

MSC:

 32A17 Special families of functions of several complex variables 32A36 Bergman spaces of functions in several complex variables
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References:

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