{"title":"关于函数模的分数阶光滑性","authors":"Dong Li","doi":"10.4208/aam.oa-2021-0006","DOIUrl":null,"url":null,"abstract":"We consider the Nemytskii operators $u\\to |u|$ and $u\\to u^{\\pm}$ in a bounded domain $\\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\\Omega)$ with $0\\le s<3/2$.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Fractional Smoothness of Modulus of Functions\",\"authors\":\"Dong Li\",\"doi\":\"10.4208/aam.oa-2021-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the Nemytskii operators $u\\\\to |u|$ and $u\\\\to u^{\\\\pm}$ in a bounded domain $\\\\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\\\\Omega)$ with $0\\\\le s<3/2$.\",\"PeriodicalId\":58853,\"journal\":{\"name\":\"应用数学年刊:英文版\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"应用数学年刊:英文版\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.4208/aam.oa-2021-0006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学年刊:英文版","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4208/aam.oa-2021-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the Nemytskii operators $u\to |u|$ and $u\to u^{\pm}$ in a bounded domain $\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\Omega)$ with $0\le s<3/2$.
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