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Journal of Function Spaces and Applications
Volume 2013, Article ID 593521, 10 pages
http://dx.doi.org/10.1155/2013/593521
Research Article

The Fractional Carleson Measures on the Unit Ball of

1College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
2College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China

Received 7 March 2013; Accepted 9 May 2013

Academic Editor: Kehe Zhu

Copyright © 2013 Dongfang Wang and Bolin Ma. 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. L. Carleson, “An interpolation problem for bounded analytic functions,” The American Journal of Mathematics, vol. 80, pp. 921–930, 1958. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. B. Garnett, Bounded Analytic Functions, vol. 96, Academic Press, New York, NY, USA, 1981. View at MathSciNet
  3. R. Aulaskari, J. Xiao, and R. H. Zhao, “On subspaces and subsets of BMOA and UBC,” Analysis, vol. 15, no. 2, pp. 101–121, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Wu and C. Xie, “Q spaces and Morrey spaces,” Journal of Functional Analysis, vol. 201, no. 1, pp. 282–297, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Xiao, Holomorphic Q Classes, vol. 1767 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. A. Cima and W. R. Wogen, “A Carleson measure theorem for the Bergman space on the ball,” Journal of Operator Theory, vol. 7, no. 1, pp. 157–165, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, Fla, USA, 1995. View at MathSciNet
  8. W. W. Hastings, “A Carleson measure theorem for Bergman spaces,” Proceedings of the American Mathematical Society, vol. 52, pp. 237–241, 1975. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D. H. Luecking, “Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives,” The American Journal of Mathematics, vol. 107, no. 1, pp. 85–111, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Pérez-González and J. Rättyä, “Forelli-Rudin estimates, Carleson measures and F(p,q,s)-functions,” Journal of Mathematical Analysis and Applications, vol. 315, no. 2, pp. 394–414, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Arazy, S. D. Fisher, and J. Peetre, “Möbius invariant function spaces,” Journal für die Reine und Angewandte Mathematik, vol. 363, pp. 110–145, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. Aulaskari, D. A. Stegenga, and J. Xiao, “Some subclasses of BMOA and their characterization in terms of Carleson measures,” The Rocky Mountain Journal of Mathematics, vol. 26, no. 2, pp. 485–506, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Wu, “A new characterization for Carleson measures and some applications,” Integral Equations and Operator Theory, vol. 71, no. 2, pp. 161–180, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Kotilainen, V. Latvala, and J. Rättyä, “Carleson measures and conformal self-mappings in the real unit ball,” Mathematische Nachrichten, vol. 281, no. 11, pp. 1582–1589, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. A. Nolder, “A characterization of certain measures using quasiconformal mappings,” Proceedings of the American Mathematical Society, vol. 109, no. 2, pp. 349–356, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. V. Ahlfors, Möbius Transformations in Several Dimensions, Ordway Professorship Lectures in Mathematics, University of Minnesota School of Mathematics, Minneapolis, Minn, USA, 1981. View at Zentralblatt MATH · View at MathSciNet
  17. G. D. Anderson, M. K. Vamanamurthy, and M. K. Vuorinen, Conformal Invariants, Inequalities, and Quasiconformal Maps, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, NY, USA, 1997. View at Zentralblatt MATH · View at MathSciNet
  18. L. K. Hua, Starting with the Unit Circle, Springer, New York, NY, USA; Science Press, Beijing, China, 1981. View at MathSciNet
  19. M. Vuorinen, Conformal Geometry and Quasiregular Mappings, vol. 1319 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1988. View at MathSciNet
  20. Z. Wu, “Area operator on Bergman spaces,” Science in China A, vol. 49, no. 7, pp. 987–1008, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. R. R. Coifman and G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Springer, New York, NY, USA, 1971. View at MathSciNet
  22. P. L. Duren, “Extension of a theorem of Carleson,” Bulletin of the American Mathematical Society, vol. 75, pp. 143–146, 1969. View at Google Scholar · View at MathSciNet