{"title":"Multidimensional analogues of the refined versions of Bohr inequalities involving Schwarz mappings","authors":"Shanshan Jia, Ming-Sheng Liu, Saminathan Ponnusamy","doi":"arxiv-2409.10091","DOIUrl":null,"url":null,"abstract":"Our first aim of this article is to establish several new versions of refined\nBohr inequalities for bounded analytic functions in the unit disk involving\nSchwarz functions. Secondly, %as applications of these results, we obtain\nseveral new multidimensional analogues of the refined Bohr inequalities for\nbounded holomorphic mappings on the unit ball in a complex Banach space\ninvolving higher dimensional Schwarz mappings. All the results are proved to be\nsharp.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10091","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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