{"title":"A New Approach for Hardy Spaces on Euclidean Space","authors":"Youhai Huang, Qiquan Fang, Xiangxing Tao, Taotao Zheng","doi":"10.1007/s12220-024-01749-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we develop a new approach to the classical Hardy spaces on Euclidean space. The new ideas of this paper are (i) introduce new test functions and distributions; (ii) we use the classical Calderón reproducing formula on <span>\\(L^2({\\mathbb {R}}^d)\\)</span> only; (iii) the Hardy space is defined by the collections of all new distributions with the classical wavelet-type representation and the norms of Hardy space are defined as the norms of the classical atomic Hardy spaces.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01749-9","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 develop a new approach to the classical Hardy spaces on Euclidean space. The new ideas of this paper are (i) introduce new test functions and distributions; (ii) we use the classical Calderón reproducing formula on \(L^2({\mathbb {R}}^d)\) only; (iii) the Hardy space is defined by the collections of all new distributions with the classical wavelet-type representation and the norms of Hardy space are defined as the norms of the classical atomic Hardy spaces.
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