Toeplitz operators on the Dirichlet space of \(\mathbb B_n\) (Q1938344)
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scientific article; zbMATH DE number 6134201
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Toeplitz operators on the Dirichlet space of \(\mathbb B_n\) |
scientific article; zbMATH DE number 6134201 |
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Toeplitz operators on the Dirichlet space of \(\mathbb B_n\) (English)
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4 February 2013
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The authors study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball of \(\mathbb{B}_n\). By direct calculation, they characterize pluriharmonic symbols for which the corresponding Toeplitz operator is normal or isometric, and obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Also, the commuting problem of Toeplitz operators whose symbols are of the form \(z^p\bar{z}^q\phi(|z|^2)\) is studied.
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Toeplitz operator
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Dirichlet space
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pluriharmonic function
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normal operator
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isometric operator
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commuting operator
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