Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

Authors
Guan, Hong Yan Lu, Yu Feng
Citation
Guan, Hong Yan et Lu, Yu Feng, Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space, Acta mathematica Sinica. English series (Print) , 30(8), 2014, pp. 1395-1406
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
8
Year of publication
2014
Pages
1395 - 1406
Database
ACNP
SICI code
Abstract
In this paper, we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C. We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator. Meanwhile, we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.