Bulletin of the Belgian Mathematical Society - Simon Stevin

Sequences of some meromorphic function spaces

M. A. Bakhit and A. El-Sayed Ahmed

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Abstract

Our goal in this paper is to introduce some new sequences of some meromorphic function spaces, which will be called $b_q$ and $q_{K}$-sequences. Our study is motivated by the theories of normal, $Q^{\#}_K$ and meromorphic Besov functions. For a non-normal function $f$ the sequences of points $\{a_n\}$ and $\{b_n\}$ for which $$\lim_{n\rightarrow \infty}(1-|a_n|^2)f^{\#}(a_n)=+\infty\,\,\,\mbox{and} $$ $$ \lim_{n\rightarrow\infty}\iint_\Delta \bigl(f^{\#}(z)\bigr)^q (1-|z|^2)^{q-2}(1-|\varphi_{a_n}(z)|^2)^s dA(z)=+\infty\;$$ or $$ \lim_{n\rightarrow\infty}\iint_\Delta \bigl(f^{\#}(z)\bigr)^2 K(z,a_n)dA(z)=+\infty\;$$ are considered and compared with each other. Finally, non-normal meromorphic functions are described in terms of the distribution of the values of these meromorphic functions.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 3 (2009), 395-408.

Dates
First available in Project Euclid: 1 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1251832367

Digital Object Identifier
doi:10.36045/bbms/1251832367

Mathematical Reviews number (MathSciNet)
MR2566824

Zentralblatt MATH identifier
1176.30085

Subjects
Primary: 30D45: Bloch functions, normal functions, normal families 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
$b_q, q_K$ -sequences meromorphic functions Besov classes

Citation

El-Sayed Ahmed, A.; Bakhit, M. A. Sequences of some meromorphic function spaces. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 3, 395--408. doi:10.36045/bbms/1251832367. https://projecteuclid.org/euclid.bbms/1251832367


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