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Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces

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  • Hidetaka Hamada

Abstract

Let BH$\mathbb {B}_H$ be the unit ball of a complex Hilbert space H. First, we give a Bohr's inequality for the holomorphic mappings with lacunary series with values in complex Hilbert balls. Next, we give several results on Bohr's inequality for pluriharmonic mappings with values in ℓ2. Note that the Bohr phenomenons that we have obtained are completely different from those in the case with values in C$\mathbb {C}$ and are sharp in the case with values in ℓ2.

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  • Hidetaka Hamada, 2023. "Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 2795-2808, July.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:7:p:2795-2808
    DOI: 10.1002/mana.202100537
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    References listed on IDEAS

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    1. Yusuf Abu Muhanna & Rosihan M. Ali & Saminathan Ponnusamy, 2017. "On the Bohr Inequality," Springer Optimization and Its Applications, in: Narendra Kumar Govil & Ram Mohapatra & Mohammed A. Qazi & Gerhard Schmeisser (ed.), Progress in Approximation Theory and Applicable Complex Analysis, pages 269-300, Springer.
    2. Ilgiz R Kayumov & Saminathan Ponnusamy & Nail Shakirov, 2018. "Bohr radius for locally univalent harmonic mappings," Mathematische Nachrichten, Wiley Blackwell, vol. 291(11-12), pages 1757-1768, August.
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