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Indexed by:Journal Papers

Date of Publication:2015-07-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE、Scopus

Volume:58

Issue:7

Page Number:1461-1472

ISSN No.: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) .