Duke Mathematical Journal

Characterization of Schatten-class Hankel operators on weighted Bergman spaces

Jordi Pau

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Abstract

We completely characterize the simultaneous membership in the Schatten ideals Sp, 0<p< of the Hankel operators Hf and Hf¯ on the Bergman space, in terms of the behavior of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.

Article information

Source
Duke Math. J., Volume 165, Number 14 (2016), 2771-2791.

Dates
Received: 25 March 2015
Revised: 27 October 2015
First available in Project Euclid: 23 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1466703840

Digital Object Identifier
doi:10.1215/00127094-3627310

Mathematical Reviews number (MathSciNet)
MR3551773

Zentralblatt MATH identifier
06653512

Subjects
Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 30H20: Bergman spaces, Fock spaces 32A36: Bergman spaces

Keywords
Bergman spaces Hankel operators Schatten classes

Citation

Pau, Jordi. Characterization of Schatten-class Hankel operators on weighted Bergman spaces. Duke Math. J. 165 (2016), no. 14, 2771--2791. doi:10.1215/00127094-3627310. https://projecteuclid.org/euclid.dmj/1466703840


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References

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