Siberian Mathematical Journal

, Volume 46, Issue 2, pp 308–314 | Cite as

Fractional derivatives of Bloch type functions

  • Songxiao Li


Some integral characterizations of Bloch type functions are given in terms of fractional derivatives, and their characterizations in terms of Carleson type measures are also obtained.


fractional derivatives Bloch type function Carleson type measure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rudin W., Function Theory in the Unit Ball of ℂn, Springer-Verlag, New York (1980).Google Scholar
  2. 2.
    Ouyang C. H., Yang W. S., and Zhao R. H., “Möbius invariant Q p spaces associated with the Green’s function on the unit ball of ℂn,” Pacific J. Math, 182, No.1, 69–99 (1998).Google Scholar
  3. 3.
    Ouyang C. H., Yang W. S., and Zhao R. H., “Characterizations of Bergman spaces and Bloch spaces in the unit ball of ℂn,” Trans. Amer. Math. Soc., 347, No.11, 4301–4313 (1995).Google Scholar
  4. 4.
    Xu H. M., “A class of characterizations of α-Bloch functions in the unit ball,” Adv. Math. (Chinese edition), 32, No.5, 580–584 (2003).Google Scholar
  5. 5.
    Ouyang C. H., “α-Carleson measure and Bloch functions on bounded symmetric domains of ℂn,” Acta Math. Sci., 15, 385–393 (1995).Google Scholar
  6. 6.
    Yang W. S., “Vanishing Carleson type measure characterizations of Q p,0,” C. R. Math. Rep. Acad. Sci. Canada, 21, 1–5 (1999).Google Scholar
  7. 7.
    Timoney R. M., “Bloch functions in several complex variables,” Bull. London Math. Soc., 12, 241–267 (1980).Google Scholar
  8. 8.
    Boo R. C. and Kyung S. R., “Fractional derivatives of Bloch functions, growth rate, and interpolation,” Acta Math. Hungar., 72, No.1–2, 67–86 (1996).Google Scholar
  9. 9.
    Li Bo and Ouyang C. H., “Higher radial derivative of Bloch type functions,” Acta Math. Sci., 22, No.4, 433–445 (2002).Google Scholar
  10. 10.
    Zhuo W. X. and Yang W. S., “Integral criteria of Bloch type functions on radial derivative,” Acta Math. Sci. (Chinese edition), 18, 451–458 (1998).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Songxiao Li
    • 1
  1. 1.JiaYing UniversityGuangDongChina

Personalised recommendations