{"title":"与扭曲拉普拉斯算子相关的谱投影的夏普$L^p$-$L^q$估计","authors":"Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu","doi":"10.5565/publmat6622210","DOIUrl":null,"url":null,"abstract":"In this note we are concerned with estimates for the spectral projection operator $\\mathcal{P}_\\mu$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\\mathcal{P}_\\mu$ from $L^p$ to $L^q$ when $1\\le p\\le 2\\le q\\le \\infty$. As an application, we obtain uniform resolvent estimate for $L$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Sharp $L^p$-$L^q$ estimate fof the spectral projection associated with the twisted Laplacian\",\"authors\":\"Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu\",\"doi\":\"10.5565/publmat6622210\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we are concerned with estimates for the spectral projection operator $\\\\mathcal{P}_\\\\mu$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\\\\mathcal{P}_\\\\mu$ from $L^p$ to $L^q$ when $1\\\\le p\\\\le 2\\\\le q\\\\le \\\\infty$. As an application, we obtain uniform resolvent estimate for $L$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/publmat6622210\",\"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/publmat6622210","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sharp $L^p$-$L^q$ estimate fof the spectral projection associated with the twisted Laplacian
In this note we are concerned with estimates for the spectral projection operator $\mathcal{P}_\mu$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\mathcal{P}_\mu$ from $L^p$ to $L^q$ when $1\le p\le 2\le q\le \infty$. As an application, we obtain uniform resolvent estimate for $L$.
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