{"title":"The Kohn–Laplacian and Cauchy–Szegö projection on model domains","authors":"D. Chang, Ji Li, Jingzhi Tie, Qingyan Wu","doi":"10.4310/amsa.2023.v8.n1.a4","DOIUrl":null,"url":null,"abstract":"We study the Kohn-Laplacian and its fundamental solution on some model domains in $\\mathbb C^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szeg\\\"o projections on these model domains using the real analysis method. We further show that these Cauchy-Szeg\\\"o kernels are Calder\\'on-Zygmund kernels under the suitable quasi-metric.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematical Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/amsa.2023.v8.n1.a4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 2
Abstract
We study the Kohn-Laplacian and its fundamental solution on some model domains in $\mathbb C^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szeg\"o projections on these model domains using the real analysis method. We further show that these Cauchy-Szeg\"o kernels are Calder\'on-Zygmund kernels under the suitable quasi-metric.