{"title":"对“BMO函数均值的连续性和某些奇异积分的Calderon-Zygmund性质”的修正和注释","authors":"K. Yabuta","doi":"10.5036/BFSIU1968.16.53","DOIUrl":null,"url":null,"abstract":"These are singular integrals of Calderon type, related to the Cauchy integral. Then, quite recently, Murai [2] has shown that T1 and T2 are bounded on L2(R). On the other hand, as in our former paper [3], one can easily check that the kernels in the above singular integrals satisfy the desired conditions (3.1), (3.2) and (3.3) in [3]. Hence they are Calderon-Zygmund singular integral operators. Finally we note that, because of the Calderon-Zygmund property, weighted norm inequalities hold for them, i.e., if 1<p<∞ and w(x)∈Ap(R), then","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"396 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1984-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Correction and Remark to \\\"Continuity of the mean values of BMO functions and Calderon-Zygmund properties of certain singular integrals\\\"\",\"authors\":\"K. Yabuta\",\"doi\":\"10.5036/BFSIU1968.16.53\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"These are singular integrals of Calderon type, related to the Cauchy integral. Then, quite recently, Murai [2] has shown that T1 and T2 are bounded on L2(R). On the other hand, as in our former paper [3], one can easily check that the kernels in the above singular integrals satisfy the desired conditions (3.1), (3.2) and (3.3) in [3]. Hence they are Calderon-Zygmund singular integral operators. Finally we note that, because of the Calderon-Zygmund property, weighted norm inequalities hold for them, i.e., if 1<p<∞ and w(x)∈Ap(R), then\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"396 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1984-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.16.53\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.16.53","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Correction and Remark to "Continuity of the mean values of BMO functions and Calderon-Zygmund properties of certain singular integrals"
These are singular integrals of Calderon type, related to the Cauchy integral. Then, quite recently, Murai [2] has shown that T1 and T2 are bounded on L2(R). On the other hand, as in our former paper [3], one can easily check that the kernels in the above singular integrals satisfy the desired conditions (3.1), (3.2) and (3.3) in [3]. Hence they are Calderon-Zygmund singular integral operators. Finally we note that, because of the Calderon-Zygmund property, weighted norm inequalities hold for them, i.e., if 1
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