{"title":"卡诺群上有界（1，σ）-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":"10.3103/s1066369x24700208","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper we study the locally uniform convergence of homeomorphisms with bounded <span>\\((1,\\sigma )\\)</span>-weighted <span>\\((q,p)\\)</span>-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded <span>\\((1,\\sigma )\\)</span>-weighted <span>\\((q,p)\\)</span>-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"40 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower Semicontinuity of Distortion Coefficients for Homeomorphisms of Bounded (1, σ)-Weighted (q, p)-Distortion on Carnot Groups\",\"authors\":\"S. K. Vodopyanov, D. A. Sboev\",\"doi\":\"10.3103/s1066369x24700208\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this paper we study the locally uniform convergence of homeomorphisms with bounded <span>\\\\((1,\\\\sigma )\\\\)</span>-weighted <span>\\\\((q,p)\\\\)</span>-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded <span>\\\\((1,\\\\sigma )\\\\)</span>-weighted <span>\\\\((q,p)\\\\)</span>-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.</p>\",\"PeriodicalId\":46110,\"journal\":{\"name\":\"Russian Mathematics\",\"volume\":\"40 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s1066369x24700208\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700208","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Lower Semicontinuity of Distortion Coefficients for Homeomorphisms of Bounded (1, σ)-Weighted (q, p)-Distortion on Carnot Groups
Abstract
In this paper we study the locally uniform convergence of homeomorphisms with bounded \((1,\sigma )\)-weighted \((q,p)\)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded \((1,\sigma )\)-weighted \((q,p)\)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.
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