{"title":"Bohr phenomenon on the unit ball of a complex Banach space","authors":"H. Hamada, Tatsuhiro Honda, Y. Mizota","doi":"10.7153/mia-2020-23-98","DOIUrl":null,"url":null,"abstract":"Let BX be the unit ball of a complex Banach space X . In this paper, we will generalize several results related to the Bohr radius for analytic functions or harmonic functions on the unit disc U in C to holomorphic mappings or pluriharmonic mappings on BX . We will establish Bohr’s inequality for the class of holomorphic mappings which are subordinate to convex mappings on BX . Next, we will establish Bohr’s inequality for pluriharmonic mappings on BX . We will also obtain the p -Bohr radius for bounded pluriharmonic functions on BX . Finally, we will determine the Bohr radius for a class of holomorphic functions on BX which contains odd holomorphic functions on BX . Mathematics subject classification (2010): 32A05, 32A10, 32K05.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"118 1","pages":"1325-1341"},"PeriodicalIF":0.9000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/mia-2020-23-98","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Let BX be the unit ball of a complex Banach space X . In this paper, we will generalize several results related to the Bohr radius for analytic functions or harmonic functions on the unit disc U in C to holomorphic mappings or pluriharmonic mappings on BX . We will establish Bohr’s inequality for the class of holomorphic mappings which are subordinate to convex mappings on BX . Next, we will establish Bohr’s inequality for pluriharmonic mappings on BX . We will also obtain the p -Bohr radius for bounded pluriharmonic functions on BX . Finally, we will determine the Bohr radius for a class of holomorphic functions on BX which contains odd holomorphic functions on BX . Mathematics subject classification (2010): 32A05, 32A10, 32K05.
期刊介绍：
''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.
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