{"title":"关于平移不变凸微分基的比较","authors":"Irakli Japaridze","doi":"10.1515/gmj-2023-2070","DOIUrl":null,"url":null,"abstract":"It is known that if <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2070_eq_0070.png\" /> <jats:tex-math>{B^{\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2070_eq_0070.png\" /> <jats:tex-math>{B^{\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> differentiate the integrals of the same class of non-negative functions. We show that under the same conditions it is not possible to assert more about similarity of the differential properties of <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2070_eq_0070.png\" /> <jats:tex-math>{B^{\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> in view of their positive equivalence.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"81 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the comparison of translation invariant convex differentiation bases\",\"authors\":\"Irakli Japaridze\",\"doi\":\"10.1515/gmj-2023-2070\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is known that if <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2070_eq_0070.png\\\" /> <jats:tex-math>{B^{\\\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2070_eq_0070.png\\\" /> <jats:tex-math>{B^{\\\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> differentiate the integrals of the same class of non-negative functions. We show that under the same conditions it is not possible to assert more about similarity of the differential properties of <jats:italic>B</jats:italic> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mi>B</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2070_eq_0070.png\\\" /> <jats:tex-math>{B^{\\\\prime}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> in view of their positive equivalence.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":\"81 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2023-2070\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2070","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: 0
摘要
众所周知，如果 B 和 B ′ {B^{/prime}} 是平移不变的凸密度微分基，并且与它们相关的最大算子在局部上相互大化，那么 B 和 B ′ {B^{/prime} 就微分同一类非负函数的积分。我们证明，在同样的条件下，鉴于 B 和 B ′ {B^{prime} 的正等价性，不可能断言它们的微分性质有更多的相似性。
On the comparison of translation invariant convex differentiation bases
It is known that if B and B′{B^{\prime}} are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then B and B′{B^{\prime}} differentiate the integrals of the same class of non-negative functions. We show that under the same conditions it is not possible to assert more about similarity of the differential properties of B and B′{B^{\prime}} in view of their positive equivalence.
期刊介绍：
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
