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arXiv · 2610.05194

Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc

Goutam Haldar·Kawsar Ali·Sujoy Majumder·Dilip Chandra Pramanik
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Abstract

In this paper, we investigate Bohr-type inequalities for certain integral transforms of some bounded holomorphic operator-valued functions defined on a shifted disc. More precisely, we consider functions $f\in H^{\infty}(Ω_γ,\mathcal{B}(\mathcal{H}))$, where $\mathcal{B}(\mathcal{H})$ denotes the space of bounded linear operators on a complex Hilbert space $\mathcal{H}$, and study the Bohr phenomena associated with the series representations in \eqref{e1.2a} and \eqref{e2.1}. Moreover, we determine the sharp radii $R_γ>0$ for which the corresponding majorant series satisfy the required inequalities for all $|z|\leq R_γ$. One of our main results extends some recent result due to Kumar and Sahoo \cite{Kumar-Sahoo-Meditarr-2023} to a large extent, and the other one is new in the literature

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Goutam Haldar, Kawsar Ali, Sujoy Majumder, Dilip Chandra Pramanik. 2026-10-04. Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc. https://arxiv.org/abs/2610.05194

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