Abstract
AbstractLet 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 and are sharp in the case with values in ℓ2.
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