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Multidimensional analogues of the refined versions of Bohr inequalities involving Schwarz mappings (2409.10091v1)
Published 16 Sep 2024 in math.CV
Abstract: Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, %as applications of these results, we obtain several new multidimensional analogues of the refined Bohr inequalities for bounded holomorphic mappings on the unit ball in a complex Banach space involving higher dimensional Schwarz mappings. All the results are proved to be sharp.