{"title":"欧几里得空间上的哈代空间新方法","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":"{\"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}","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}
A New Approach for Hardy Spaces on Euclidean Space
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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