Illinois Journal of Mathematics

Algebraic properties of small Hankel operators on the harmonic Bergman space

Yong Chen, Wei He, and Yunzhong Hu

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Abstract

This paper completely characterizes the commuting problem of two small Hankel operators acting on the harmonic Bergman space with the symbols one being bounded and another being quasihomogeneous, or both being harmonic. The characterizations for semi-commuting problem and the product of two small Hankel operators being another small Hankel operator for certain class of symbols are also obtained.

Article information

Source
Illinois J. Math., Volume 59, Number 2 (2015), 295-317.

Dates
Received: 7 June 2014
Revised: 29 January 2016
First available in Project Euclid: 5 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1462450702

Digital Object Identifier
doi:10.1215/ijm/1462450702

Mathematical Reviews number (MathSciNet)
MR3499513

Zentralblatt MATH identifier
1342.47037

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 31A05: Harmonic, subharmonic, superharmonic functions

Citation

Chen, Yong; He, Wei; Hu, Yunzhong. Algebraic properties of small Hankel operators on the harmonic Bergman space. Illinois J. Math. 59 (2015), no. 2, 295--317. doi:10.1215/ijm/1462450702. https://projecteuclid.org/euclid.ijm/1462450702


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