Characterization of Schatten-class Hankel operators on weighted Bergman spaces

Jordi Pau

doi:10.1215/00127094-3627310

Abstract

We completely characterize the simultaneous membership in the Schatten ideals $S_{p}$ , $0\lt p\lt \infty$ of the Hankel operators $H_{f}$ and $H_{\overline{f}}$ on the Bergman space, in terms of the behavior of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.

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Jordi Pau. "Characterization of Schatten-class Hankel operators on weighted Bergman spaces." Duke Math. J. 165 (14) 2771 - 2791, 1 October 2016. https://doi.org/10.1215/00127094-3627310

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Received: 25 March 2015; Revised: 27 October 2015; Published: 1 October 2016

First available in Project Euclid: 23 June 2016

zbMATH: 06653512

MathSciNet: MR3551773

Digital Object Identifier: 10.1215/00127094-3627310

Subjects:

Primary: 47B10 , 47B35

Secondary: 30H20 , ‎32A36‎

Keywords: Bergman spaces , Hankel operators , Schatten classes

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