Bohr's theorem for Cesáro operator and certain integral transforms over octonions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917137840340992 |
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| author | Ahamed, Molla Basir Ahammed, Sabir |
| author_facet | Ahamed, Molla Basir Ahammed, Sabir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bohr's theorem for Cesáro operator and certain integral transforms over octonions Ahamed, Molla Basir Ahammed, Sabir Complex Variables 30A10, 30B10, 30G35, 30H05, 44A10, 44A55 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. |
| title | Bohr's theorem for Cesáro operator and certain integral transforms over octonions |
| topic | Complex Variables 30A10, 30B10, 30G35, 30H05, 44A10, 44A55 |
| url | https://arxiv.org/abs/2512.09933 |