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A New Characterization for Carleson Measures and Some Applications

  • Zhijian Wu
Article

Abstract

We provide a new characterization for Carleson measures in terms of the L p behaviors of certain functions represented as an integration on a non-tangential cone. Applications for characterizing the boundedness and compactness of Volterra type operators from Hardy spaces to some holomorphic spaces are also presented.

Mathematics Subject Classification (2010)

Primary 47B38 Secondary 32A35 

Keywords

Carleson measures Hardy spaces Caldersón–Zygmund decomposition 

References

  1. 1.
    Aleksandrov A.B., Peller V.V.: Hankel operators and similarity to a contraction. Internat. Math. Res. Notices 6, 263–275 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aleman A., Cima J.A.: An Integral Operator on \({\mathcal{H}^p}\) and Hardy’s Inequality J. Anal. Math. 85, 157–176 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Carleson L.: An interpolation problem for bounded analytic functions. Amer. J. Math. 80, 921–930 (1958)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Cohn W.S.: Generalized area operators on Hardy spaces. J. Math. Anal. Appl. 216(1), 112–121 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Duren P.L.: Extension of a theorem of Carleson. Bull. Amer. Math. Soc. 75, 143–146 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Garnett J.B.: Bounded Analytic Functions. Academic Press, New York (1982)Google Scholar
  7. 7.
    Gong M., Lou Z., Wu Z.: Area Operators from \({\mathcal{H}^p}\) Spaces to L q Spaces. Sci. China. 53(2), 357–366 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Wu Z.: Area operator on Bergman spaces. Sci. China Ser. A Math. 49(7), 987–1008 (2006)zbMATHCrossRefGoogle Scholar
  9. 9.
    Wu Z., Xie C.: Q spaces and Morrey spaces. J. Funct. Anal. 201(1), 282–297 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Xiao J.: Holomorphic Q Classes. Lecture notes in mathematics, 1767. Springer-Verlag, Berlin (2001)Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AlabamaTuscaloosaUSA

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