{"title":"一致可整流集上L^p$空间的$\\ α $数刻划","authors":"Jonas Azzam, Damian Dąbrowski","doi":"10.5565/PUBLMAT6722313","DOIUrl":null,"url":null,"abstract":"We give a characterization of $L^{p}(\\sigma)$ for uniformly rectifiable measures $\\sigma$ using Tolsa's $\\alpha$-numbers, by showing, for $1<p<\\infty$ and $f\\in L^{p}(\\sigma)$, that \r\n\\[ \r\n\\lVert f\\rVert_{L^{p}(\\sigma)}\\sim \\left\\lVert\\left(\\int_{0}^{\\infty} \\left(\\alpha_{f\\sigma}(x,r)+|f|_{x,r}\\alpha_{\\sigma}(x,r)\\right)^2\\ \\frac{dr}{r} \\right)^{\\frac{1}{2}}\\right\\rVert_{L^{p}(\\sigma)}. \r\n\\]","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"An $\\\\alpha$-number characterization of $L^p$ spaces on uniformly rectifiable sets\",\"authors\":\"Jonas Azzam, Damian Dąbrowski\",\"doi\":\"10.5565/PUBLMAT6722313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a characterization of $L^{p}(\\\\sigma)$ for uniformly rectifiable measures $\\\\sigma$ using Tolsa's $\\\\alpha$-numbers, by showing, for $1<p<\\\\infty$ and $f\\\\in L^{p}(\\\\sigma)$, that \\r\\n\\\\[ \\r\\n\\\\lVert f\\\\rVert_{L^{p}(\\\\sigma)}\\\\sim \\\\left\\\\lVert\\\\left(\\\\int_{0}^{\\\\infty} \\\\left(\\\\alpha_{f\\\\sigma}(x,r)+|f|_{x,r}\\\\alpha_{\\\\sigma}(x,r)\\\\right)^2\\\\ \\\\frac{dr}{r} \\\\right)^{\\\\frac{1}{2}}\\\\right\\\\rVert_{L^{p}(\\\\sigma)}. \\r\\n\\\\]\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/PUBLMAT6722313\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/PUBLMAT6722313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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