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

Bappaditya Bhowmik; Sambhunath Sen

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 2, page 397-414
  • ISSN: 0011-4642

Abstract

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It is known that if f is holomorphic in the open unit disc 𝔻 of the complex plane and if, for some c > 0 , | f ( z ) | ≤ 1 / ( 1 - | z | 2 ) c , z ∈ 𝔻 , then | f ' ( z ) | ≤ 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 𝔻 . In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.

How to cite

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Bhowmik, Bappaditya, and Sen, Sambhunath. "Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions." Czechoslovak Mathematical Journal 74.2 (2024): 397-414. <http://eudml.org/doc/299583>.

@article{Bhowmik2024,
abstract = {It is known that if $f$ is holomorphic in the open unit disc $\{\mathbb \{D\}\}$ of the complex plane and if, for some $c>0$, $|f(z)|\le 1/(1-|z|^2)^c$, $z\in \{\mathbb \{D\}\}$, then $|f^\{\prime \}(z)|\le 2(c+1)/(1-|z|^2)^\{c+1\}$. 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.},
author = {Bhowmik, Bappaditya, Sen, Sambhunath},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bloch function; meromorphic function; Landau's reduction; Taylor coefficient},
language = {eng},
number = {2},
pages = {397-414},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions},
url = {http://eudml.org/doc/299583},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Bhowmik, Bappaditya
AU - Sen, Sambhunath
TI - Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 2
SP - 397
EP - 414
AB - It is known that if $f$ is holomorphic in the open unit disc ${\mathbb {D}}$ of the complex plane and if, for some $c>0$, $|f(z)|\le 1/(1-|z|^2)^c$, $z\in {\mathbb {D}}$, then $|f^{\prime }(z)|\le 2(c+1)/(1-|z|^2)^{c+1}$. 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.
LA - eng
KW - Bloch function; meromorphic function; Landau's reduction; Taylor coefficient
UR - http://eudml.org/doc/299583
ER -

References

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