Finite rank Toeplitz products with harmonic symbols |
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| Authors: | Boo Rim Choe Hyungwoon Koo |
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| Affiliation: | a Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea
b Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea |
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| 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. |
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| Keywords: | Finite rank Toeplitz operator Harmonic symbol Bergman space |
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