Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions

Bhowmik, Bappaditya ; Sen, Sambhunath

Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 397-414

Abstract (VO)

It is known that if $f$ is holomorphic in the open unit disc ${\mathbb D}$ of the complex plane and if, for some $c>0$, $|f(z)|\leq 1/(1-|z|^2)^c$, $z\in {\mathbb D}$, then $|f'(z)|\leq 2(c+1)/(1-|z|^2)^{c+1}$. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in ${\mathbb D}$. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.

Détail

DOI : 10.21136/CMJ.2024.0332-23

Classification : 30C50, 30C99, 30D45
Keywords: Bloch function; meromorphic function; Landau's reduction; Taylor coefficient

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