Hankel operators in the Bergman space and Schatten \(p\)-classes: The case \(1<p<2\) (Q2750851)
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scientific article; zbMATH DE number 1663096
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hankel operators in the Bergman space and Schatten \(p\)-classes: The case \(1<p<2\) |
scientific article; zbMATH DE number 1663096 |
Statements
21 October 2001
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Hankel operators
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Bergman space
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Schatten class
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mean oscillation
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Hankel operators in the Bergman space and Schatten \(p\)-classes: The case \(1<p<2\) (English)
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It is known that the Hankel operators \(H_f\) and \(H_{\overline f}\) on the Bergman space belong to the Schatten class \(C_p\) if and only if the mean oscillation \(M0(f)(z)= \{|\widetilde f|^2(z)- |\widetilde f(z)|^2\}^{1/2}\) belongs to \(L^p(D;(1-|z|^2)^{-2} dA(z))\) for \(2\leq p<\infty\). This paper proves the same result also holds when \(1< p< 2\).
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