<p>In this paper, we derive the sharp Bohr type inequalities for the Cesáro operator, Bernardi integral operator, discrete Fourier transform and discrete Laplace transform acting on the class of bounded analytic functions defined on shifted disks <Equation ID="Equ8"> <EquationSource Format="TEX">$\begin{aligned} \Omega _{\gamma }=\left\{ z\in \mathbb {C}:\left| z+\frac{\gamma }{1-\gamma }\right| <\frac{1}{1-\gamma }\right\} \quad \text {for}\quad \gamma \in [0,1).\end{aligned}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <msub> <mi mathvariant="normal">Ω</mi> <mi>γ</mi> </msub> <mo>=</mo> <mfenced close="}" open="{"> <mi>z</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> <mo>:</mo> <mfenced close="|" open="|"> <mi>z</mi> <mo>+</mo> <mfrac> <mi>γ</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>γ</mi> </mrow> </mfrac> </mfenced> <mo><</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>-</mo> <mi>γ</mi> </mrow> </mfrac> </mfenced> <mspace width="1em" /> <mtext>for</mtext> <mspace width="1em" /> <mi>γ</mi> <mo>∈</mo> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation></p>

Bohr type inequalities for certain integral operators and transforms on shifted disks

期刊论文
发表日期：

2026年1月16日

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Vasudevarao Allu,
Raju Biswas,
Rajib Mandal

摘要

In this paper, we derive the sharp Bohr type inequalities for the Cesáro operator, Bernardi integral operator, discrete Fourier transform and discrete Laplace transform acting on the class of bounded analytic functions defined on shifted disks $\begin{aligned} \Omega _{\gamma }=\left\{ z\in \mathbb {C}:\left| z+\frac{\gamma }{1-\gamma }\right| <\frac{1}{1-\gamma }\right\} \quad \text {for}\quad \gamma \in [0,1).\end{aligned}$ $\begin{matrix} Ω_{γ} = \{z \in C : |z + \frac{γ}{1 - γ}| < \frac{1}{1 - γ}\} for γ \in [0, 1) . \end{matrix}$