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Bounded Hankel Products on the Bergman Space of the Polydisk

  Published:2009-02-01
 Printed: Feb 2009
  • Yufeng Lu
  • Shuxia Shang
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Abstract

We consider the problem of determining for which square integrable functions $f$ and $g$ on the polydisk the densely defined Hankel product $H_{f}H_g^\ast$ is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products $H_{g}T_{\bar{f}}$ and $T_{f}H_{g}^{*}$, where $f$ and $g$ are square integrable on the polydisk and $f$ is analytic.
Keywords: Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydisk Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydisk
MSC Classifications: 47B35, 47B47 show english descriptions Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Commutators, derivations, elementary operators, etc.
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
47B47 - Commutators, derivations, elementary operators, etc.
 

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