{"title":"索博列夫代数反例","authors":"T. Coulhon, Luke G. Rogers","doi":"10.4171/JFG/59","DOIUrl":null,"url":null,"abstract":"In the Euclidean setting the Sobolev spaces $W^{\\alpha,p}\\cap L^\\infty$ are algebras for the pointwise product when $\\alpha>0$ and $p\\in(1,\\infty)$. This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices $\\alpha,p$.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2016-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/59","citationCount":"0","resultStr":"{\"title\":\"Sobolev algebra counterexamples\",\"authors\":\"T. Coulhon, Luke G. Rogers\",\"doi\":\"10.4171/JFG/59\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the Euclidean setting the Sobolev spaces $W^{\\\\alpha,p}\\\\cap L^\\\\infty$ are algebras for the pointwise product when $\\\\alpha>0$ and $p\\\\in(1,\\\\infty)$. This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices $\\\\alpha,p$.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2016-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/JFG/59\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/JFG/59\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fractal Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JFG/59","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In the Euclidean setting the Sobolev spaces $W^{\alpha,p}\cap L^\infty$ are algebras for the pointwise product when $\alpha>0$ and $p\in(1,\infty)$. This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices $\alpha,p$.
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