Algebraic properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space

In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a noncons...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2008-11, Vol.24 (11), p.1843-1852
Main Authors: Yu, Tao, Wu, Shi Yue
Format: Article
Language:English
Subjects:
Algebra
Commuting
Dirichlet problem
Hilbert space
Mathematics
Mathematics and Statistics
Studies
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Summary:In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for S φ S ψ = S φψ .
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-008-7266-1