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Part of the book series: Operator Theory Advances and Applications ((OT,volume 114))

Abstract

A new class of functions named Q p has been recently introduced and studied by several mathematicians. These spaces are situated between the classical Dirichlet space D 1 and the Bloch space B, where B is in a sense maximal among Möbius invariant function spaces. Further, the spaces Q p as a function of parameter values p fill the gap between D 1 and B and join these well-known spaces by certain values of p. Now we will show some features of this research.

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References

  1. R. Aulaskari and G. Csordas, Besov spaces and the Q q ,o classes, Acta Sci. Math., 60, (1995) 31–48.

    MathSciNet  MATH  Google Scholar 

  2. R. Aulaskari and P. Lappan, Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal, Complex analysis and its applications, Editors C.-C. Yang et al., Pitman Res. Notes Math. Ser., 305, Longman, Harlow, (1994) 136–146.

    Google Scholar 

  3. R. Aulaskari, P. Lappan, J. Xiao and R. Zhao, On α-Bloch spaces and multipliers of Dirichlet spaces, J. Math. Anal. Appl., 209, (1997) 103–121

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Aulaskari, D. A. Stegenga and J. Xiao, Some subclasses of BMOA and their characterization in terms of Carleson measures, Rocky Mountain J. Math., 26, (1996) 485–506.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Aulaskari, D. A. Stegenga and R. Zhao, Random power series and Q p , Proc. 16th Rolf Nevanlinna Colloquium, Editors I. Laine and O. Martio, de Gruyter, Berlin (1996) 247–255.

    Google Scholar 

  6. R. Aulaskari, J. Xiao and R. Zhao, On subspaces and subsets of BMOA and UBC, Analysis, 15, (1995) 101–121.

    MathSciNet  MATH  Google Scholar 

  7. A. Baernstein II, Analytic functions of bounded mean oscillation, Aspects of contemporary complex analysis, Editors D. A. Brannan and J. G. Clunie, Academic Press, London, (1980) 2–26.

    Google Scholar 

  8. W. G. Cochran, J. H. Shapiro and D. C. Ullrich, Random Dirichlet functions: multipliers and smoothness, Canad. J. Math., 45, (1993) 255–268.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Essen and J. Xiao, Some results on Q p spaces, 0 < p < 1, J. Reine Angew. Math., 485, (1997) 173–195.

    MathSciNet  MATH  Google Scholar 

  10. M. Mateljevic and M. Pavlovic, L P -behaviour of power series with positive coefficients and Hardy spaces, Proc. Amer. Math. Soc., 87, (1983) 309–316.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Miao, A property of analytic functions with Hadamard gaps, Bull. Austral. Math. Soc., 45, (1992) 105–112.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc., 207, (1975) 391–405.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. T. Sledd and D. A. Stegenga, An H 1 multiplier theorem, Ark. Mat., 19, (1981) 265–270.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Zygmund, Trigonometric series, Cambridge Univ. Press, London (1959).

    MATH  Google Scholar 

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Aulaskari, R. (2000). On Q p functions. In: de Arellano, E.R., Vasilevski, N.L., Shapiro, M., Tovar, L.M. (eds) Complex Analysis and Related Topics. Operator Theory Advances and Applications, vol 114. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8698-7_3

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  • DOI: https://doi.org/10.1007/978-3-0348-8698-7_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9734-1

  • Online ISBN: 978-3-0348-8698-7

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