{"title":"Weighted weak-type inequalities for square functions","authors":"A. Osȩkowski","doi":"10.7153/mia-2020-23-21","DOIUrl":null,"url":null,"abstract":"The paper is devoted to weighted weak-type inequalities for square functions of continuous-path martingales and identifies the optimal dependence of the weak norm on the characteristic of the weight. The proof rests on Bellman function technique: the estimates are deduced from the existence of special functions enjoying appropriate size conditions and concavity. Mathematics subject classification (2010): 46E30, 60G42.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"267-286"},"PeriodicalIF":0.9000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/mia-2020-23-21","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: 1
Abstract
The paper is devoted to weighted weak-type inequalities for square functions of continuous-path martingales and identifies the optimal dependence of the weak norm on the characteristic of the weight. The proof rests on Bellman function technique: the estimates are deduced from the existence of special functions enjoying appropriate size conditions and concavity. Mathematics subject classification (2010): 46E30, 60G42.
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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