Abstract
For a non-normal function/the sequences of points {a n } and {b n } for which \( {\lim_{{n \to \infty }}}(1 - {\left| {{a_n}} \right|^2}){f^{\# }}({a_n}) = + \infty \) and \( {\lim_{{n \to \infty }}}\iint {_{\Delta }{{({f^{\# }}(z))}^2}{g^p}(z,{a_n})dA(z) = + \infty } \) are considered and compared with each other.
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References
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, Pitman Research Notes in Mathematics, 305, Longman Scientific & Technical Harlow, 1994, 136–146.
R. Aulaskari, H. Wulan and R. Zhao, Carleson measure and some classes of meromorphic functions, Proc. Amer. Math. Soc, Vol. 128, 2000, 2329–2335.
R. Aulaskari, J. Xiao and R. Zhao, On subspaces and subsets of BMOA and UBC, Analysis, Vol. 15, 1995, 101–121.
D. Campbell and G. Wickes, Characterizations of normal meromorphic functions, Complex Analysis, Joensuu 1978, 55–72, Lecture Notes in Mathematics, 747, Springer-Verlag, Berlin.
A. Baernstein II, Analytic functions of bounded mean oscillation, Aspects of contemporary complex analysis, Academic Press, London, 1980, 3–36.
M. Essén, Q p -spaces, Lectures at the summer school on “Complex Function Spaces” at Mekrijärvi Aug.30 – Sept.l, 1999. To appear, Department of Mathematics, University of Joensuu, Finland.
J. L. Schiff, Normal families, Springer-Verlag, New York, 1993.
H. Wulan, On some classes of meromorphic functions, Ann. Acad. Sci. Fenn. Math. Diss., Vol. 116, 1998, 1–57.
S. Yamashita, Functions of uniformly bounded characteristic, Ann. Acad. Sci. Fenn. Ser. A I Math., Vol. 7, 1982, 349–367.
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© 2004 Kluwer Academic Publishers
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Aulaskari, R., Makhmutov, S., Wulan, H. (2004). On Q p Sequences. In: Le, H.S., Tutschke, W., Yang, C.C. (eds) Finite or Infinite Dimensional Complex Analysis and Applications. Advances in Complex Analysis and Its Applications, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0221-6_7
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DOI: https://doi.org/10.1007/978-1-4613-0221-6_7
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