About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 151929, 9 pages
http://dx.doi.org/10.1155/2013/151929
Research Article

Weighted Differentiation Composition Operators to Bloch-Type Spaces

1Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra 182320, India

Received 2 February 2013; Accepted 8 April 2013

Academic Editor: Pedro M. Lima

Copyright © 2013 Junming Liu 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. P. L. Duren, Theory of Hp Spaces, vol. 38 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1970. View at MathSciNet
  2. H. T. Kaptanoğlu and S. Tülü, “Weighted Bloch, Lipschitz, Zygmund, Bers, and growth spaces of the ball: Bergman projections and characterizations,” Taiwanese Journal of Mathematics, vol. 15, no. 1, pp. 101–127, 2011. View at Zentralblatt MATH · View at MathSciNet
  3. K. Zhu, “Bloch type spaces of analytic functions,” The Rocky Mountain Journal of Mathematics, vol. 23, no. 3, pp. 1143–1177, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. Zhu, Operator Theory in Function Spaces, vol. 138 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2nd edition, 2007. View at MathSciNet
  5. D. Girela, “Analytic functions of bounded mean oscillation,” in Complex Function Spaces (Mekrijärvi, 1999), vol. 4 of University of Joensuu, Department of Mathematics. Report Series, pp. 61–170, University of Joensuu, Joensuu, Finland, 2001. View at Zentralblatt MATH · View at MathSciNet
  6. X. Zhu, “Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces,” Integral Transforms and Special Functions, vol. 18, no. 3-4, pp. 223–231, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Zhu, “Generalized weighted composition operators on weighted Bergman spaces,” Numerical Functional Analysis and Optimization, vol. 30, no. 7-8, pp. 881–893, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. A. Hibschweiler and N. Portnoy, “Composition followed by differentiation between Bergman and Hardy spaces,” The Rocky Mountain Journal of Mathematics, vol. 35, no. 3, pp. 843–855, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Ohno, “Products of composition and differentiation between Hardy spaces,” Bulletin of the Australian Mathematical Society, vol. 73, no. 2, pp. 235–243, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 Zentralblatt MATH · View at MathSciNet
  11. S. Ohno, “Products of differentiation and composition on Bloch spaces,” Bulletin of the Korean Mathematical Society, vol. 46, no. 6, pp. 1135–1140, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Stević, “Characterizations of composition followed by differentiation between Bloch-type spaces,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4312–4316, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Wu and H. Wulan, “Products of differentiation and composition operators on the Bloch space,” Collectanea Mathematica, vol. 63, no. 1, pp. 93–107, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. A. K. Sharma, “Generalized composition operators between weighted Bergman spaces,” Acta Scientiarum Mathematicarum, vol. 78, pp. 187–211, 2012.
  15. A. Sharma and A. K. Sharma, “Carleson measures and a class of generalized integration operators on the Bergman space,” The Rocky Mountain Journal of Mathematics, vol. 41, no. 5, pp. 1711–1724, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. K. Sharma, “Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces,” Turkish Journal of Mathematics, vol. 35, no. 2, pp. 275–291, 2011. View at Zentralblatt MATH · View at MathSciNet
  17. S. Stević, “Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces,” Applied Mathematics and Computation, vol. 211, no. 1, pp. 222–233, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Stević, “Weighted differentiation composition operators from H and Bloch spaces to nth weighted-type spaces on the unit disk,” Applied Mathematics and Computation, vol. 216, no. 12, pp. 3634–3641, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. Stević and A. K. Sharma, “Iterated differentiation followed by composition from Bloch-type spaces to weighted BMOA spaces,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3574–3580, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. S. Stević and A. K. Sharma, “Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk,” Annales Polonici Mathematici, vol. 105, no. 1, pp. 77–86, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. Y. Yu and Y. Liu, “Weighted differentiation composition operators from H to Zygmund spaces,” Integral Transforms and Special Functions, vol. 22, no. 7, pp. 507–520, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. 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
  23. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. 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
  25. J. S. Manhas and R. Zhao, “New estimates of essential norms of weighted composition operators between Bloch type spaces,” Journal of Mathematical Analysis and Applications, vol. 389, no. 1, pp. 32–47, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  26. O. Hyvärinen and M. Lindström, “Estimates of essential norms of weighted composition operators between Bloch-type spaces,” Journal of Mathematical Analysis and Applications, vol. 393, no. 1, pp. 38–44, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  27. H. Wulan, D. Zheng, and K. Zhu, “Compact composition operators on BMOA and the Bloch space,” Proceedings of the American Mathematical Society, vol. 137, no. 11, pp. 3861–3868, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. R. Zhao, “Essential norms of composition operators between Bloch type spaces,” Proceedings of the American Mathematical Society, vol. 138, no. 7, pp. 2537–2546, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. J. Liu and C. Xiong, “Norm-attaining integral operators on analytic function spaces,” Journal of Mathematical Analysis and Applications, vol. 399, no. 1, pp. 108–115, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. R. Aulaskari, M. Nowak, and R. Zhao, “The nth derivative characterisation of Möbius invariant Dirichlet space,” Bulletin of the Australian Mathematical Society, vol. 58, no. 1, pp. 43–56, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. R. Zhao, “Distances from Bloch functions to some Möbius invariant spaces,” Annales Academiae Scientiarum Fennicae, vol. 33, no. 1, pp. 303–313, 2008. View at Zentralblatt MATH · View at MathSciNet
  32. 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 MathSciNet
  33. M. Tjani, Compact composition operators on some Möbius invariant Banach spaces [Ph.D. thesis], Michigan State University, 1996.