Toeplitz products on the vector weighted Bergman spaces

被引:0
作者
Gonessa J. [1 ,2 ]
Sehba B.F. [3 ,4 ]
机构
[1] Université de Bangui, Département de Mathématiques et Informatique, BP. 908, Bangui-République Centrafricaine
[2] LATP, UM.R. CNRS. 6632, Université de Provence, 39 Rue F-Juliot-Curie, Marseille Cedex 13
[3] Department of Mathematics, University of Ghana, Legon, P. O. Box LG 62, Legon, Accra
[4] Centre de Mathématiques et Informatique (CMI), Université de Provence, Technopôle Château-Gombert, 39, rue F. Joliot Curie, Marseille Cedex 13
来源
Acta Scientiarum Mathematicarum | 2014年 / 80卷 / 3-4期
关键词
Bergman spaces; Reproducing kernel; Toeplitz operator;
D O I
10.14232/actasm-012-777-1
中图分类号
学科分类号
摘要
A result of K. Stroethoff and D. Zheng provides on the polydisk a necessary and sufficient condition for the Toeplitz product TfTg to be bounded on the unweighted Bergman space. We consider the same question on the vector weighted Bergman space of the unit polydisc. © Bolyai Institute, University of Szeged.
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页码:511 / 530
页数:19
相关论文
共 13 条
  • [1] Aleman A., Pott S., Reguera M.C., Sarason Conjecture on the Bergman Space, (2013)
  • [2] Cruz-Uribe D., Martell J.M., Perez C.M., Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture, Adv. Math., 216, pp. 647-676, (2007)
  • [3] Miao J., Bounded Toeplitz products on the weighted Bergman spaces of the unit ball, J. Math. Anal. Appl., 346, pp. 305-313, (2008)
  • [4] Michalska M., Mowak M., Sobolewski P., Bounded Toeplitz and Hankel products on weighted Bergman spaces of the unit Ball, Annales Polonici Mathematici, 99, pp. 45-53, (2010)
  • [5] Nazarov F., A Counterexample to Sarason's Conjecture
  • [6] Pott S., Strouse E., Products of Toeplitz operators on the Bergman spaces A<sup>2</sup><sub>α</sub>, Algebra i Analiz, 18, pp. 144-161, (2006)
  • [7] Rudin W., 241, (1980)
  • [8] Stroethoff K., Zheng A.D., Products of Hankel and Toeplitz operators on the Bergman space, J. Funct. Anal., 169, pp. 289-313, (1999)
  • [9] Stroethoff K., Zheng A.D., Bounded Toeplitz products on the Bergman space of the polydisk, J. Math. Anal. Appl., 278, pp. 125-135, (2003)
  • [10] Stroethoff K., Zheng A.D., Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl., 325, pp. 114-129, (2007)