{"title":"Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball","authors":"Changbao Pang, Maofa Wang, Bang Xu, Hao Zhang","doi":"arxiv-2408.13726","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate various square functions on the unit complex\nball. We prove the weighted inequalities of the Lusin area integral associated\nwith Poisson integral in terms of $A_p$ weights for all $1<p<\\infty$; this\ngives an affirmative answer to an open question raised by Segovia and Wheeden.\nTo that end, we establish the weighted inequalities for Littlewood-Paley type\nsquare functions. As an interesting application, we obtain the weighted\ninequalities of the Lusin area integral associated with Bergman gradient. In\naddition, we get an equivalent characterization of weighted Hardy spaces by\nmeans of the Lusin area integral in the context of holomorphic functions. We\nalso obtain the weighted inequalities for Volterra integral operators. The key\ningredients of our proof involve complex analysis, Calder\\'on-Zygmund theory,\nthe local mean oscillation technique and sparse domination.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-25","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-2408.13726","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
In this paper, we investigate various square functions on the unit complex
ball. We prove the weighted inequalities of the Lusin area integral associated
with Poisson integral in terms of $A_p$ weights for all $1
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