{"title":"卡诺群上有界(1, \\sigma )-加权(q, p)-失真同构的失真系数的下半连续性","authors":"S. K. Vodopyanov, D. A. Sboev","doi":"10.26907/0021-3446-2024-3-84-90","DOIUrl":null,"url":null,"abstract":"In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"23 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \\\\sigma )-weighted (q, p)-distortion on Carnot groups\",\"authors\":\"S. K. Vodopyanov, D. A. Sboev\",\"doi\":\"10.26907/0021-3446-2024-3-84-90\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.\",\"PeriodicalId\":507800,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"volume\":\"23 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26907/0021-3446-2024-3-84-90\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2024-3-84-90","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \sigma )-weighted (q, p)-distortion on Carnot groups
In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.
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