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.