{"title":"$overline{partial}$-有界 Lipschitz 域乘积的估计值","authors":"Song-Ying Li, Sujuan Long, Jie Lao","doi":"arxiv-2409.00293","DOIUrl":null,"url":null,"abstract":"Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In\nthe paper, we construct an integral solution operator $T[f]$ for any\n$\\overline{\\partial}$ closed $(0,1)$-form $f\\in L^p_{(0,1)}(D^n)$ solving the\nCauchy-Riemain equation $\\overline{\\partial} u=f$ on the product domains $D^n$\nand obtain the $L^p$-estimates for all $1<p\\le \\infty$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"178 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$\\\\overline{\\\\partial}$-Estimates on the product of bounded Lipschitz domain\",\"authors\":\"Song-Ying Li, Sujuan Long, Jie Lao\",\"doi\":\"arxiv-2409.00293\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In\\nthe paper, we construct an integral solution operator $T[f]$ for any\\n$\\\\overline{\\\\partial}$ closed $(0,1)$-form $f\\\\in L^p_{(0,1)}(D^n)$ solving the\\nCauchy-Riemain equation $\\\\overline{\\\\partial} u=f$ on the product domains $D^n$\\nand obtain the $L^p$-estimates for all $1<p\\\\le \\\\infty$.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"178 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.00293\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00293","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
$\overline{\partial}$-Estimates on the product of bounded Lipschitz domain
Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In
the paper, we construct an integral solution operator $T[f]$ for any
$\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the
Cauchy-Riemain equation $\overline{\partial} u=f$ on the product domains $D^n$
and obtain the $L^p$-estimates for all $1