Bohr's theorem for Cesáro operator and certain integral transforms over octonions
Authors
Molla Basir Ahamed
Sabir Ahammed
Abstract
In this paper, we first establish the Bohr's theorem for Cesáro operator defined for $f\in \mathcal{SRB}(\mathbb{B})$ of slice regular functions in the open unit ball $\mathbb{B}$ of the largest alternative division algebras of octonions $\mathbb{O}$, such that $|f(x)| \leq 1$ for all $x \in \mathbb{B}$. Next, we establish Bohr type inequalities for Bernardi operator for the functions $f\in \mathcal{SRB}(\mathbb{B})$, and with the help of this, we obtain Bohr type inequality for Libera operator and Alexander operator. Finally, we obtain Bohr-type inequalities for certain integral transforms, namely Fourier (discrete) and Laplace (discrete) transforms for $f\in \mathcal{SRB}(\mathbb{B}).$ All the results are proven to be sharp.
