Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 989625, 10 pages
http://dx.doi.org/10.1155/2011/989625
Research Article

Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane

1Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
2School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, J & K Katra 182320, India
3Department of Mathematics, University of Jammu, Jammu 180006, India

Received 25 January 2011; Accepted 3 May 2011

Academic Editor: Narcisa C. Apreutesei

Copyright © 2011 Stevo Stević et al. 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. 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.
  2. V. Matache, “Composition operators on Hp of the upper half-plane,” Analele Universităţii din Timişoara, Seria Ştiinţe Matematice, vol. 27, no. 1, pp. 63–66, 1989. View at Google Scholar
  3. V. Matache, “Composition operators on Hardy spaces of a half-plane,” Proceedings of the American Mathematical Society, vol. 127, no. 5, pp. 1483–1491, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. H. J. Schwartz, Composition operators on Hp, Ph.D. thesis, University of Toledo, Ohio, USA, 1969.
  5. J. H. Shapiro and W. Smith, “Hardy spaces that support no compact composition operators,” Journal of Functional Analysis, vol. 205, no. 1, pp. 62–89, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. K. Sharma and S. D. Sharma, “Weighted composition operators between Bergman-type spaces,” Communications of the Korean Mathematical Society, vol. 21, no. 3, pp. 465–474, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. D. Sharma, A. K. Sharma, and S. Ahmed, “Carleson measures in a vector-valued Bergman space,” Journal of Analysis and Applications, vol. 4, no. 1, pp. 65–76, 2006. View at Google Scholar · View at Zentralblatt MATH
  8. S. D. Sharma, A. K. Sharma, and S. Ahmed, “Composition operators between Hardy and Bloch-type spaces of the upper half-plane,” Bulletin of the Korean Mathematical Society, vol. 44, no. 3, pp. 475–482, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. D. Sharma, A. K. Sharma, and Z. Abbas, “Weighted composition operators on weighted vector-valued Bergman spaces,” Applied Mathematical Sciences, vol. 4, no. 41–44, pp. 2049–2063, 2010. View at Google Scholar
  10. 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 Google Scholar
  11. R. K. Singh and S. D. Sharma, “Composition operators on a functional Hilbert space,” Bulletin of the Australian Mathematical Society, vol. 20, no. 3, pp. 377–384, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. K. Singh and S. D. Sharma, “Noncompact composition operators,” Bulletin of the Australian Mathematical Society, vol. 21, no. 1, pp. 125–130, 1980. View at Publisher · View at Google Scholar
  13. S. Stević, “Weighted composition operators between mixed norm spaces and Hα spaces in the unit ball,” Journal of Inequalities and Applications, Article ID 28629, 9 pages, 2007. View at Google Scholar
  14. 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
  15. S. Stević, “Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 499–504, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. Stević, “Composition operators from the Hardy space to Zygmund-type spaces on the upper half-plane and the unit disc,” Journal of Computational Analysis and Applications, vol. 12, no. 2, pp. 305–312, 2010. View at Google Scholar
  17. S. Stević, “Composition operators from the Hardy space to the n-th weighted-type space on the unit disk and the half-plane,” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3950–3955, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. S. Stević, “Composition operators from the weighted Bergman space to the n-th weighted-type space on the upper half-plane,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3379–3384, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. S.-I. Ueki, “Hilbert-Schmidt weighted composition operator on the Fock space,” International Journal of Mathematical Analysis, vol. 1, no. 13–16, pp. 769–774, 2007. View at Google Scholar · View at Zentralblatt MATH
  20. S.-I. Ueki, “Weighted composition operators on the Bargmann-Fock space,” International Journal of Modern Mathematics, vol. 3, no. 3, pp. 231–243, 2008. View at Google Scholar · View at Zentralblatt MATH
  21. S.-I. Ueki, “Weighted composition operators on some function spaces of entire functions,” Bulletin of the Belgian Mathematical Society Simon Stevin, vol. 17, no. 2, pp. 343–353, 2010. View at Google Scholar · View at Zentralblatt MATH
  22. X. Zhu, “Weighted composition operators from area Nevanlinna spaces into Bloch spaces,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4340–4346, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. F. Forelli, “The isometries of Hpspaces,” Canadian Journal of Mathematics, vol. 16, pp. 721–728, 1964. View at Publisher · View at Google Scholar
  24. C. J. Kolaski, “Isometries of weighted Bergman spaces,” Canadian Journal of Mathematics, vol. 34, no. 4, pp. 910–915, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. 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
  26. S. Stević, “On a new operator from H to the Bloch-type space on the unit ball,” Utilitas Mathematica, vol. 77, pp. 257–263, 2008. View at Google Scholar
  27. S. Stević, “On an integral operator from the Zygmund space to the Bloch-type space on the unit ball,” Glasgow Mathematical Journal, vol. 51, no. 2, pp. 275–287, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. S. Stević, “On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball,” Journal of Mathematical Analysis and Applications, vol. 354, no. 2, pp. 426–434, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. S. Stević, “On an integral operator between Bloch-type spaces on the unit ball,” Bulletin des Sciences Mathématiques, vol. 134, no. 4, pp. 329–339, 2010. View at Google Scholar
  30. 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
  31. K. L. Avetisyan, “Integral representations in general weighted Bergman spaces,” Complex Variables, vol. 50, no. 15, pp. 1151–1161, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. K. L. Avetisyan, “Hardy-Bloch type spaces and lacunary series on the polydisk,” Glasgow Mathematical Journal, vol. 49, no. 2, pp. 345–356, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  33. K. D. Bierstedt and W. H. Summers, “Biduals of weighted Banach spaces of analytic functions,” Australian Mathematical Society Journal Series A, vol. 54, no. 1, pp. 70–79, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH