Bounded Toeplitz products on the weighted Bergman spaces of the unit ball |
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Authors: | Jie Miao |
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Affiliation: | Department of Mathematics and Statistics, Arkansas State University, PO Box 70, State University, AR 72467, USA |
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Abstract: | Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved. |
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Keywords: | Toeplitz operator Reproducing kernel Bounded operator |
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