Commuting dual Toeplitz operators on the harmonic Dirichlet space

Authors
Yang, Jing Yu Hu, Yin Yin Lu, Yu Feng Yu, Tao
Citation
Yang, Jing Yu et al., Commuting dual Toeplitz operators on the harmonic Dirichlet space, Acta mathematica Sinica. English series (Print) , 32(9), 2016, pp. 1099-1105
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
9
Year of publication
2016
Pages
1099 - 1105
Database
ACNP
SICI code
Abstract
In this paper, we characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for ., . . W 1,., S . S . = S . S . on (D h ). if and only if . and . satisfy one of the following conditions: (1) Both . and . are harmonic functions; (2) There exist complex constants . and ., not both 0, such that . = ..+..