@article{Liu2024, 
author = {Lijun Liu},
title = {Dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {25413-25437},
keywords = {dual Toeplitz operator, harmonic Bergman space, zero-product problem, commutativity},
url = {https://www.sciopen.com/article/10.3934/math.20241241},
doi = {10.3934/math.20241241},
abstract = {This paper aimed to give some partial answers to the zero-product problem and commutativity problem concerning dual Toeplitz operators with nonharmonic symbols on the orthogonal complement of the harmonic Bergman space. Using the symbol map, we described the necessary condition for  Sφ1Sφ2⋯SφN=0 with radial symbols. Furthermore, we established the sufficient and necessary conditions for  SφSψ=SψSφ with  φ(z)=azp1z¯q1+bzp2z¯q2 and  ψ(z)=zsz¯t.}
}