Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2016-09-01

Journal: ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals: Scopus、ISTIC、SCIE

Volume: 32

Issue: 9

Page Number: 1099-1105

ISSN: 1439-8516

Key Words: Dual Toeplitz operator; harmonic Dirichlet space; commutativity

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 phi, psi is an element of W (1,infinity), S phi S psi = S psi S phi on (D-h )(perpendicular to) if and only if phi and psi satisfy one of the following conditions: (1) Both phi and psi are harmonic functions; (2) There exist complex constants alpha and beta, not both 0, such that phi = alpha psi+beta.