Finite rank Toeplitz products with harmonic symbols

Boo Rim Choe; Hyungwoon Koo; Young Joo Lee

doi:10.1016/j.jmaa.2008.01.019

Finite rank Toeplitz products with harmonic symbols

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

On the Bergman space of the unit ball of Cⁿ, we study the finite rank problem for Toeplitz products with harmonic symbols. We first solve the problem with two factors in case symbols have local continuous extension property up to the boundary. Also, in case symbols have additional Lipschitz continuity up to (some part of) the boundary, we solve the problem for multiple products with number of factors depending on the dimension n. Analogous theorems on the polydisk are also obtained.

Original language	English
Pages (from-to)	81-98
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	343
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2008.01.019
Publication status	Published - 2008 Jul 1

Keywords

Bergman space
Finite rank
Harmonic symbol
Toeplitz operator

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2008.01.019

Cite this

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title = "Finite rank Toeplitz products with harmonic symbols",

abstract = "On the Bergman space of the unit ball of Cn, we study the finite rank problem for Toeplitz products with harmonic symbols. We first solve the problem with two factors in case symbols have local continuous extension property up to the boundary. Also, in case symbols have additional Lipschitz continuity up to (some part of) the boundary, we solve the problem for multiple products with number of factors depending on the dimension n. Analogous theorems on the polydisk are also obtained.",

keywords = "Bergman space, Finite rank, Harmonic symbol, Toeplitz operator",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Lee, {Young Joo}",

note = "Funding Information: This research was supported by KOSEF (R01-2003-000-10243-0). Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), leeyj@chonnam.ac.kr (Y.J. Lee).",

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T1 - Finite rank Toeplitz products with harmonic symbols

AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Lee, Young Joo

N1 - Funding Information: This research was supported by KOSEF (R01-2003-000-10243-0). Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), leeyj@chonnam.ac.kr (Y.J. Lee).

PY - 2008/7/1

Y1 - 2008/7/1

N2 - On the Bergman space of the unit ball of Cn, we study the finite rank problem for Toeplitz products with harmonic symbols. We first solve the problem with two factors in case symbols have local continuous extension property up to the boundary. Also, in case symbols have additional Lipschitz continuity up to (some part of) the boundary, we solve the problem for multiple products with number of factors depending on the dimension n. Analogous theorems on the polydisk are also obtained.

AB - On the Bergman space of the unit ball of Cn, we study the finite rank problem for Toeplitz products with harmonic symbols. We first solve the problem with two factors in case symbols have local continuous extension property up to the boundary. Also, in case symbols have additional Lipschitz continuity up to (some part of) the boundary, we solve the problem for multiple products with number of factors depending on the dimension n. Analogous theorems on the polydisk are also obtained.

KW - Bergman space

KW - Finite rank

KW - Harmonic symbol

KW - Toeplitz operator

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DO - 10.1016/j.jmaa.2008.01.019

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AN - SCOPUS:41449114932

SN - 0022-247X

VL - 343

SP - 81

EP - 98

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Finite rank Toeplitz products with harmonic symbols

Abstract

Keywords

ASJC Scopus subject areas

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