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Abstract and Applied Analysis
Volume 2008, Article ID 279691, 11 pages
http://dx.doi.org/10.1155/2008/279691
Research Article

Essential Norms of Weighted Composition Operators from the -Bloch Space to a Weighted-Type Space on the Unit Ball

Mathematical Institute of the Serbian Academy of Sciences and Arts, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 8 May 2008; Accepted 5 September 2008

Academic Editor: Simeon Reich

Copyright © 2008 Stevo Stević. 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. A. L. Shields and D. L. Williams, “Bonded projections, duality, and multipliers in spaces of analytic functions,” Transactions of the American Mathematical Society, vol. 162, pp. 287–302, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Stević, “Weighted composition operators between mixed norm spaces and Hα spaces in the unit ball,” Journal of Inequalities and Applications, vol. 2007, Article ID 28629, 9 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. Tang, “Weighted composition operators between Bers-type spaces and Bergman spaces,” Applied Mathematics. A Journal of Chinese Universities B, vol. 22, no. 1, pp. 61–68, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. D. D. Clahane and S. Stević, “Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball,” Journal of Inequalities and Applications, vol. 2006, Article ID 61018, 11 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  6. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, vol. 226 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2005. View at Zentralblatt MATH · View at MathSciNet
  7. X. Fu and X. Zhu, “Weighted composition operators on some weighted spaces in the unit ball,” Abstract and Applied Analysis, vol. 2008, Article ID 605807, 8 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. P. Gorkin and B. D. MacCluer, “Essential norms of composition operators,” Integral Equations and Operator Theory, vol. 48, no. 1, pp. 27–40, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Li and S. Stević, “Composition followed by differentiation between Bloch type spaces,” Journal of Computational Analysis and Applications, vol. 9, no. 2, pp. 195–205, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Li and S. Stević, “Weighted composition operators from Bergman-type spaces into Bloch spaces,” Proceedings of the Indian Academy of Sciences. Mathematical Sciences, vol. 117, no. 3, pp. 371–385, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. Li and S. Stević, “Weighted composition operators from α-Bloch space to H on the polydisc,” Numerical Functional Analysis and Optimization, vol. 28, no. 7-8, pp. 911–925, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Li and S. Stević, “Weighted composition operators from H to the Bloch space on the polydisc,” Abstract and Applied Analysis, vol. 2007, Article ID 48478, 13 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Li and S. Stević, “Generalized composition operators on Zygmund spaces and Bloch type spaces,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1282–1295, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Li and S. Stević, “Weighted composition operators between H and α-Bloch space in the unit ball,” to appear in Taiwanese Journal of Mathematics.
  15. L. Luo and S.-I. Ueki, “Weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of n,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 88–100, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. B. D. MacCluer and R. Zhao, “Essential norms of weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 4, pp. 1437–1458, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. Montes-Rodríguez, “Weighted composition operators on weighted Banach spaces of analytic functions,” Journal of the London Mathematical Society, vol. 61, no. 3, pp. 872–884, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Ohno, “Weighted composition operators between H and the Bloch space,” Taiwanese Journal of Mathematics, vol. 5, no. 3, pp. 555–563, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. Ohno, K. Stroethoff, and R. Zhao, “Weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 1, pp. 191–215, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. Shi and L. Luo, “Composition operators on the Bloch space of several complex variables,” Acta Mathematica Sinica, vol. 16, no. 1, pp. 85–98, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Stević, “Composition operators between H and α-Bloch spaces on the polydisc,” Zeitschrift für Analysis und ihre Anwendungen, vol. 25, no. 4, pp. 457–466, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. Stević, “Norm of weighted composition operators from Bloch space to Hμ on the unit ball,” Ars Combinatoria, vol. 88, pp. 125–127, 2008. View at Google Scholar
  23. S.-I. Ueki and L. Luo, “Compact weighted composition operators and multiplication operators between Hardy spaces,” Abstract and Applied Analysis, vol. 2008, Article ID 196498, 12 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  24. X. Zhu, “Generalized weighted composition operators from Bloch type spaces to weighted Bergman spaces,” Indian Journal of Mathematics, vol. 49, no. 2, pp. 139–150, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. X. Zhu, “Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces,” Integral Transforms and Special Functions, vol. 18, no. 3, pp. 223–231, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. S. Stević, “On an integral operator on the unit ball in n,” Journal of Inequalities and Applications, vol. 2005, no. 1, pp. 81–88, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. S. Li and S. Stević, “Riemann-Stieltjes-type integral operators on the unit ball in n,” Complex Variables and Elliptic Equations, vol. 52, no. 6, pp. 495–517, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. Stević, “Boundedness and compactness of an integral operator on a weighted space on the polydisc,” Indian Journal of Pure and Applied Mathematics, vol. 37, no. 6, pp. 343–355, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. S. Stević, “Boundedness and compactness of an integral operator in a mixed norm space on the polydisk,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 48, no. 3, pp. 694–706, 2007. View at Google Scholar · View at MathSciNet