On characterizations of isometries on function spaces

Article
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Abstract

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B n in ℂ n .

Keywords

ismometry Besov spaces 

MSC(2000)

32A17 47A15 
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References

  1. 1.
    Forelli F. The isometries of H p. Canad J Math, 16: 721–728 (1964)MATHMathSciNetGoogle Scholar
  2. 2.
    Rudin W. L p-isometries and equimeasurability. Indiana Univ Math J, 3: 215–228 (1976)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Koranyi A, Vagi S. On isometries of H p of bounded symmetric domains. Canad J Math, 28: 334–340 (1976)MATHMathSciNetGoogle Scholar
  4. 4.
    Kolaski C. Isometries of Bergman space over bounded Runge domains. Canad J Math, 33: 1157–1164 (1981)MATHMathSciNetGoogle Scholar
  5. 5.
    Kolaski C. Isometries of weighted Bergman space. Canad J Math, 34: 910–915 (1982)MATHMathSciNetGoogle Scholar
  6. 6.
    Cima A, Wogen W. On isometries of Bloch space. Illinois J Math, 24: 313–316 (1980)MATHMathSciNetGoogle Scholar
  7. 7.
    Krantz S G, Ma D. On isometric isomorphisms of the Bloch spaces on the unit ball of ℂn. Michigan Math J, 36: 173–180 (1989)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chen L, Operators on the Bloch and Bergman Spaces of Several Complex Variables. PhD Thesis. Invine: University of California at Irvine, 1994Google Scholar
  9. 9.
    Li S Y. Composition operators and isometries on holomorphic function spaces over domains in ℂn. AMS/IP Stud Adv Math, 39: 161–174 (2007)MATHGoogle Scholar
  10. 10.
    Beatrous F, Li S Y. On the boundedness and compactness of operators of Hankel type. J Funct Anal, 111: 350–379 (1993)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Coifman R, Rochberg R, Weiss G. Factorization theorem for Hardy spaces in several variables. Ann of Math, 103: 611–635 (1976)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Krantz S G, Li S Y. A Note on Hardy spaces and functions of bounded mean oscillation on domains in ℂn. Michigan Math J, 41 51–72 (1994)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Krantz S G, Li S Y. Duality theorems on Hardy and Bergman spaces on convex domains of finite type in ℂn. Ann Inst Fourier, 45: 1305–1327 (1995)MATHMathSciNetGoogle Scholar
  14. 14.
    Krantz S G, Li S Y. On the decomposition theorems for Hardy spaces in domains in ℂn and application. J Fourier Anal Appl, 2: 65–107 (1995)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Li S Y, Luo W. Characterizations for Besov spaces and applications, Part I. J Math Analy Appl, 310: 477–491 (2005)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Li S Y, Luo W. Analysis on Besov spaces II: embedding and duality theorems. J Math Anal Appl, 333(2): 1189–1202 (2007)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Li S Y. Some function theoretical results on domains in ℂn. In: Proceeding of ICCM 2001, Lin C S, Yang L, Yau S T eds. Boston: International Press, 2004Google Scholar
  18. 18.
    Krantz S G, Li S Y, Rochberg R. Analysis of some function spaces associated to Hankel operators. Illinois J Math, 41 398–411 (1997)MATHMathSciNetGoogle Scholar
  19. 19.
    Li S Y. Trace Ideal criteria for composition operators on Bergman spaces. Amer J Math, 117: 1299–1324 (1995)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Nehari Z. On the bounded bilinear forms. Ann of Math, 65: 153–162 (1957)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Ouyang C, Yang W, Zhao R. Möbius invariant Q p spaces associated with the Green’s function the unit ball of ℂn. Pacific J Math, 182: 69–99 (1998)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Peloso M M. Möbius Invariant spaces on the ball. Michigan Math J, 39: 509–536 (1992)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Rudin W. The Function Theory in Unit Ball in ℂn. New York: Springer-Verlag, 1980Google Scholar
  24. 24.
    Zhou Z H, Shi J H. Compactness of composition operators on the Bloch space in classical bounded symmetric domains. Michigan Math J, 50(2): 381–405 (2002)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Zhu K. Hankel operators on Bergman spaces of bounded symmetric domains. Trans Amer Math Soc, 324: 707–730 (1991)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science Press 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouChina

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