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Indexed by:期刊论文

Date of Publication:2016-09-01

Journal:ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals:SCIE、ISTIC、Scopus

Volume:32

Issue:9

Page Number:1099-1105

ISSN No.: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.