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Lipschitz spaces and Q K type spaces

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Abstract

If f(z) = Σ ∞n=0 a n z n and g(z) = Σ ∞n=0 b n z n for functions f, g are analytic in the unit disc, the Hadamard products of f and g is defined by f * g = Σ ∞n=0 a n b n z n. In this paper, the Lipschitz spaces Λ(s, α) and Q K type spaces are studied in terms of the Hadamard products.

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References

  1. Anderson J, Clunie J, Pommerenke C. On Bloch functions and normal functions. J Reine Angew Math, 1974, 270: 12–37

    MATH  MathSciNet  Google Scholar 

  2. Aulaskari R, Girela D, Wulan H. Taylor coefficients and mean growth of the derivative of Q p functions. J Math Anal Appl, 2001, 258: 415–428

    Article  MATH  MathSciNet  Google Scholar 

  3. Beckner W. Inequalities in Fourier analysis. Ann Math, 1975, 102: 159–182

    Article  MathSciNet  Google Scholar 

  4. Duren P. Theory of H p Spaces. New York: Academic Press, 1970

    MATH  Google Scholar 

  5. Essén M, Wulan H. On analytic and meromorphic functions and spaces of Q K type. Illinois J Math, 2002, 46: 1233–1258

    MATH  MathSciNet  Google Scholar 

  6. Essén M, Wulan H, Xiao J. Several function-theoretic characterizations of Möbius invariant Q K spaces. J Funct Anal, 2006, 230: 78–115

    MATH  MathSciNet  Google Scholar 

  7. Essén M, Xiao J. Some results on Q p spaces, 0 < p < 1. J Reine Angew Math, 1997, 485: 173–195

    MATH  MathSciNet  Google Scholar 

  8. Flett T. The dual of an inequality of Hardy and Littlewood and some related inequalities. J Math Anal Appl, 1972, 38: 746–765

    Article  MATH  MathSciNet  Google Scholar 

  9. Mateljević M, Pavlović M. Multipliers of H p and BMOA. Pacific J Math, 1990, 146: 71–84

    MATH  MathSciNet  Google Scholar 

  10. Pavlović M. Hadamard product in Q p spaces. J Math Anal Appl, 2005, 305: 589–598

    Article  MATH  MathSciNet  Google Scholar 

  11. Shi J. Inequalities for the integral means of holomorphic function and their derivatives in the unit ball of ℂn. Trans Amer Math Soc, 1991, 328: 619–637

    Article  MATH  MathSciNet  Google Scholar 

  12. Wulan H, Zhang Y. Hadamard products and Q K spaces. J Math Anal Appl, 2008, 337: 1142–1150

    Article  MATH  MathSciNet  Google Scholar 

  13. Wulan H, Zhou J. Q K type spaces of analytic functions. J Func Spaces Appl, 2006, 4: 73–84

    MATH  MathSciNet  Google Scholar 

  14. Wulan H, Zhou J. The higher order derivatives of Q K type spaces. J Math Anal Appl, 2007, 332: 1216–1228

    Article  MATH  MathSciNet  Google Scholar 

  15. Xiao J. Holomorphic Q Classes. Berlin: Springer, 2001

    Book  MATH  Google Scholar 

  16. Xiao J. Geometric Qp Functions. Basel-Boston-Berlin: Birkhäuser-Verlag, 2006

    MATH  Google Scholar 

  17. Zhao R. On a general family of function spaces. Ann Aced Sci Fenn Diss, 1996, 105: 1–56

    Article  Google Scholar 

  18. Zhou J. Lacunary series in Q K type spaces. J Funct Spaces Appl, 2008, 6: 293–301

    MATH  MathSciNet  Google Scholar 

  19. Zhou J. Hadamard product in F(p, q, s). J Funct Spaces Appl, 2010, to appear

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, China

    Hao Li, Hasi Wulan & JiZhen Zhou

  2. School of Sciences, Anhui University of Science and Technology, Huainan, 232001, China

    JiZhen Zhou

Authors
  1. Hao Li
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  2. Hasi Wulan
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  3. JiZhen Zhou
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Corresponding author

Correspondence to Hasi Wulan.

Additional information

Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday

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Li, H., Wulan, H. & Zhou, J. Lipschitz spaces and Q K type spaces. Sci. China Math. 53, 771–778 (2010). https://doi.org/10.1007/s11425-010-0054-2

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  • DOI: https://doi.org/10.1007/s11425-010-0054-2

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