Some remarks on the action of Lusin area operator in Bergman spaces of the unit ball (Q2866267)
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scientific article; zbMATH DE number 6238116
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on the action of Lusin area operator in Bergman spaces of the unit ball |
scientific article; zbMATH DE number 6238116 |
Statements
13 December 2013
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Lusin area operator
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Bergman metric ball
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0.90483034
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0.88184583
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0.88025546
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0.87860096
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0.8745798
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0.8743354
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Some remarks on the action of Lusin area operator in Bergman spaces of the unit ball (English)
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Let \(B\) be the unit ball in \(\mathbb C^n\) and let \(\mu\) be a positive measure on \(B\). The Lusin area operator is defined by \(G_{\mu,\sigma}(f)(\xi)=\int_{\Gamma_\sigma(\xi)}| f(z)|,(1-| z|)^{-n},d\mu(z)\), where \(f\) is a holomorphic function on \(B\) and \(\Gamma_\sigma(\xi)=\{ z\in B:| 1-(z,\zeta)|<\sigma(1-| z|^2),\sigma>1\}\) is the Koranyi approach region with vertex \(\xi\). In this paper the Lusin area operator on weighted Bergman spaces of the unit ball is studied, using various properties of sampling sequences in the unit ball.
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