Bohr radius for invariant families of bounded analytic functions and certain Integral transforms
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917659368488960 |
|---|---|
| author | Ahamed, Molla Basir Roy, Partha Pratim Ahammed, Sabir |
| author_facet | Ahamed, Molla Basir Roy, Partha Pratim Ahammed, Sabir |
| contents | In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace (discrete) transforms of bounded analytic functions $ f(z)=\sum_{n=0}^{\infty}a_nz^n $, in a simply connected domain \begin{align*}
Ω_γ=\biggl\{z\in\mathbb{C}: \bigg|z+\dfracγ{1-γ}\bigg|<\dfrac{1}{1-γ}\;\mbox{for}\; 0\leq γ<1\biggr\},
\end{align*} where $ Ω_0=\mathbb{D} $. These results generalize some existing results. We also show that a better estimate can be obtained in radius and inequality can be shown sharp for Laplace transform of $ f $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bohr radius for invariant families of bounded analytic functions and certain Integral transforms Ahamed, Molla Basir Roy, Partha Pratim Ahammed, Sabir Complex Variables 30C45, 30C50, 30C65, 30C80 In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace (discrete) transforms of bounded analytic functions $ f(z)=\sum_{n=0}^{\infty}a_nz^n $, in a simply connected domain \begin{align*} Ω_γ=\biggl\{z\in\mathbb{C}: \bigg|z+\dfracγ{1-γ}\bigg|<\dfrac{1}{1-γ}\;\mbox{for}\; 0\leq γ<1\biggr\}, \end{align*} where $ Ω_0=\mathbb{D} $. These results generalize some existing results. We also show that a better estimate can be obtained in radius and inequality can be shown sharp for Laplace transform of $ f $. |
| title | Bohr radius for invariant families of bounded analytic functions and certain Integral transforms |
| topic | Complex Variables 30C45, 30C50, 30C65, 30C80 |
| url | https://arxiv.org/abs/2405.04040 |