Journal of Mathematical Sciences

, Volume 202, Issue 4, pp 565–572 | Cite as

Integral Reverse Estimates for Logarithmic Bloch Spaces in the Ball

  • A. N. PetrovEmail author

Integral reverse estimates for logarithmic Bloch spaces in the unit ball of m are obtained. As an application, hyperbolic gradients of inner mappings are studied.


Holomorphic Mapping Unit Ball Hardy Space Composition Operator Bloch Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. B. Aleksandrov, “Proper holomorphic mappings from the ball to the polydisk,” Dokl. Akad. Nauk SSSR, 286, 11–15 (1986).MathSciNetGoogle Scholar
  2. 2.
    A. B. Aleksandrov, J. M. Anderson, and A. Nicolau, “Inner functions, Bloch spaces, and symmetric measures,” Proc. London Math. Soc. (3), 79, 318–352 (1999).Google Scholar
  3. 3.
    E. Doubtsov, “Characterizations of the hyperbolic Nevanlinna class in the ball,” Complex Var. Elliptic Eq., 54, 119–124 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    E. Doubtsov, “Bloch-to-BMOA compositions on complex balls,” Proc. Amer. Math. Soc., 140, 4217–4225 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    E. Doubtsov, “Inner mappings, hyperbolic gradients, and composition operators,” Integral Equations Operator Theory, 73, 537–551 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M. J. González and A. Nicolau, “Multiplicative square functions,” Rev. Mat. Iberoamericana, 20, 673–736 (2004).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    M. Pavlovíc, “Lacunary series in weighted spaces of analytic functions,” Arch. Math. (Basel), 97, 467–473 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    A. N. Petrov, “Reverse estimates in logarithmic Bloch spaces,” Arch. Math. (Basel), 100, 551–560 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    W. Smith, “Inner functions in the hyperbolic little Bloch class,” Michigan Math. J., 45, 103–114 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    X. Tang, “Extended Cesàro operators between Bloch-type spaces in the unit ball of n,” J. Math. Anal. Appl., 326, 1199–1211 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    A. Zygmund, Trigonometric Series, 2nd ed., Vols. I, II, Cambridge Univ. Press, New York (1959).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St. Petersburg State University of Architecture and Civil EngineeringSt. PetersburgRussia

Personalised recommendations