Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2012, Article ID 517689, 18 pages
http://dx.doi.org/10.1155/2012/517689
Research Article

Properties of Toeplitz Operators on Some Holomorphic Banach Function Spaces

1Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
2Department of Mathematics, Faculty of Science, Taif University, P.O. Box 888, El-Hawiyah, El-Taif 5700, Saudi Arabia
3Department of Mathematics, Faculty of Science, Assiut Branch, Al-Azhar University, Assiut 32861, Egypt
4Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia

Received 5 March 2012; Accepted 18 April 2012

Academic Editor: Dashan Fan

Copyright © 2012 Ahmed El-Sayed Ahmed and Mahmoud Ali Bakhit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. T. Hahn and E. H. Youssfi, β€œMöbius invariant Besov p-spaces and Hankel operators in the Bergman space on the ball in n,” Complex Variables, vol. 17, no. 1-2, pp. 89–104, 1991. View at Google Scholar
  2. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer, New York, NY, USA, 2004.
  3. S. Li and S. Stević, β€œSome characterizations of the Besov space and the α-Bloch space,” Journal of Mathematical Analysis and Applications, vol. 346, no. 1, pp. 262–273, 2008. View at Publisher Β· View at Google Scholar
  4. W. Rudin, Function Theory in the Unit Ball of Cn, Springer, New York, NY, USA, 1980.
  5. K. Zhu, β€œPositive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains,” Journal of Operator Theory, vol. 20, no. 2, pp. 329–357, 1988. View at Google Scholar
  6. K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, NY, USA, 1990.
  7. Z. Wu, R. Zhao, and N. Zorboska, β€œToeplitz operators on Bloch-type spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 12, pp. 3531–3542, 2006. View at Publisher Β· View at Google Scholar
  8. X. Wang and T. Liu, β€œToeplitz operators on Bloch-type spaces in the unit ball of n,” Journal of Mathematical Analysis and Applications, vol. 368, no. 2, pp. 727–735, 2010. View at Publisher Β· View at Google Scholar
  9. Z. Wu, R. Zhao, and N. Zorboska, β€œToeplitz operators on analytic Besov spaces,” Integral Equations and Operator Theory, vol. 60, no. 3, pp. 435–449, 2008. View at Publisher Β· View at Google Scholar
  10. S. C. Arora and J. Bhola, β€œEssentially slant Toeplitz operators,” Banach Journal of Mathematical Analysis, vol. 3, no. 2, pp. 1–8, 2009. View at Google Scholar
  11. A. Böttcher and B. Silbermann, Analysis of Toeplitz Operators, Springer Monographs in Mathematics, Springer, Berlin, Germany, 2nd edition, 2006.
  12. C. C. Cowen and E. A. Gallardo-Gutiérrez, β€œUnitary equivalence of one-parameter groups of Toeplitz and composition operators,” Journal of Functional Analysis, vol. 261, no. 9, pp. 2641–2655, 2011. View at Publisher Β· View at Google Scholar
  13. A. V. Harutyunyan and G. Harutyunyan, β€œHolomorphic Besov spaces in the polydisc and bounded Toeplitz operators,” Analysis, vol. 30, no. 4, pp. 365–381, 2010. View at Publisher Β· View at Google Scholar
  14. T. Nakazi, β€œInvariant subspaces of Toeplitz operators and uniform algebras,” Bulletin of the Belgian Mathematical Society, vol. 15, no. 1, pp. 1–8, 2008. View at Google Scholar
  15. Y. J. Lee and N. Q. Dieu, β€œToeplitz operators on the Dirichlet spaces of planar domains,” Proceedings of the American Mathematical Society, vol. 139, no. 2, pp. 547–558, 2011. View at Publisher Β· View at Google Scholar
  16. D. Vukotić, β€œAnalytic Toeplitz operators on the Hardy space Hp: a survey,” Bulletin of the Belgian Mathematical Society, vol. 10, no. 1, pp. 101–113, 2003. View at Google Scholar