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1Department of Mathematics, Fudan University, Shanghai, P. R. China. e-mail: kyguo@fudan.edu.cn
2Institute of Mathematics, Jiaxing University, Jiaxing, Zhejiang, 314001, P. R. China. e-mail: shsun@mail.zjxu.edu.cn
3Department of Mathematics, Vanderbilt University, Nashville, TN 37240 USA. e-mail: dechao.zheng@vanderbilt.edu
4Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA. e-mail: matcyz@langate.gsu.edu
Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 628, Pages 129–168, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.021, January 2009
In this paper, we develop a machinery to study multiplication operators on the Bergman space via the Hardy space of the bidisk. Using the machinery we study the structure of reducing subspaces of a multiplication operator on the Bergman space. As a consequence, we completely classify reducing subspaces of the multiplication operator by a Blaschke product φ with order three on the Bergman space to solve a conjecture of Zhu [J. London Math. Soc. 62: 553–568, 2000].
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