Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-07-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 58

Issue: 7

Page Number: 1461-1472

ISSN: 1674-7283

Key Words: dual Toeplitz operator; harmonic Bergman space; Bergman space

Abstract: We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic phi and psi, S (phi) S (psi) = S (psi) S (phi) on (L (h) (2) )(aSyen) if and only if phi and psi satisfy one of the following conditions: (1) Both phi and psi are analytic on D. (2) Both phi and psi are anti-analytic on D. (3) There exist complex constants alpha and beta, not both 0, such that phi = alpha psi + beta. Furthermore, we give the necessary and sufficient conditions for S (phi) S (psi) = S (phi psi) .