Advertisement

Bergman-Carleson Measures and Bloch Functions on Strongly Pseudoconvex Domains

  • Hitoshi Arai
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 3)

Abstract

In their paper [4], Choa, Kim and Park proved the following characterization of Bloch functions on the unit ball B n in C n .

Keywords

Toeplitz Operator Bergman Space Pseudoconvex Domain Boundary Behavior Carleson Measure 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G. Aladro, The comparability of the Kobayashi approach region and the admissible approach region, Illinois J. of Math. 33 (1989), 42–63.MathSciNetzbMATHGoogle Scholar
  2. [2]
    H. Arai, Degenerate elliptic operators, Hardy spaces and diffusions on strongly pseudoconvex domains, Tohoku Math. J. 46 (1994), 469–498.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [31.
    H. Arai, Some characterizations of Bloch functions on strongly pseudoconvex domains, Tokyo J. Math., 17 (1994), 373–383.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. S. Choa, H. O. Kim and Y. Y. Park, A Bergman-Carleson measure characterization of Bloch functions in the unit ball of Cn, Bull. Korean Math. Soc. 29 (1992), 285–293.MathSciNetzbMATHGoogle Scholar
  5. [5]
    C. Fefferman and E. M. Stein, HP spaces of several variables, Acta Math. 129 (1972), 137–193.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    I. Graham, Boundary behavior of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in Cn with smooth boundary, Trans. Amer. Math. Soc. 207 (1975), 219–240.MathSciNetzbMATHGoogle Scholar
  7. [7]
    S. G. Krantz and D. Ma, Bloch functions on strongly pseudoconvex domains, Indiana Univ. Math. J. 37 (1988), 145–163.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    H. Li, BMO, VMO and Hankel operators on the Bergman spaces of strongly pseudoconvex domains, J. Funct. Anal. 106 (1992), 375–408.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [91.
    D.Luecking, A technique for characterizing Carleson measures on Bergman spaces, Proc. Amer. Math. Soc. (1983), 656–660.Google Scholar
  10. [10]
    D. Ma, On iterates of holomorphic maps, Math. Z. 207 (1991), 417–428.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Variables, Math. Notes, Princeton Univ. Press, 1972.Google Scholar
  12. [12]
    J. Xiao, Carleson measure, atomic decomposition and free interpolation from Bloch space, Ann. Acad. Sci. Ser. A. I. Math. 19 (1994), 175–184.Google Scholar
  13. [13]
    J. Xiao and L. Zhong, On little Bloch space, its Carleson measure, atomic decomposition and free interpolation, Complex Variables 27 (1995), 175–184.Google Scholar
  14. [14]
    K. Zhu, Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Operator Theory 20 (1988), 329–357.MathSciNetzbMATHGoogle Scholar
  15. [15]
    K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Hitoshi Arai
    • 1
  1. 1.Mathematical InstituteTohoku UniversityJapan

Personalised recommendations