Quantitative Carleman-type estimates for holomorphic sections over bounded domains

IF 1.4 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2026-09-30 DOI:10.1112/jlms.70717

Xiangsen Qin

{"title":"Quantitative Carleman-type estimates for holomorphic sections over bounded domains","authors":"Xiangsen Qin","doi":"10.1112/jlms.70717","DOIUrl":null,"url":null,"abstract":"This paper establishes quantitative Carleman-type inequalities for holomorphic sections of Hermitian vector bundles over bounded domains in <math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mi>n</mi>\n </msup>\n <annotation>$\\mathbb {C}^n$</annotation>\n </semantics></math> with <math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>⩾</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$n \\geqslant 2$</annotation>\n </semantics></math>. We first prove a Sobolev-type inequality with explicit constants for the Laplace operator, which leads to quantitative Carleman-type estimates for holomorphic functions. These results are then extended to holomorphic sections of Hermitian vector bundles satisfying certain curvature restrictions, yielding quantitative versions where previously only non-quantitative forms were available. The proofs refine existing methods through careful constant tracking and by estimating the radius of the uniform sphere condition of the boundary through the Lipschitz constant of its outward unit normal vector.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70717","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

This paper establishes quantitative Carleman-type inequalities for holomorphic sections of Hermitian vector bundles over bounded domains in $C^{n}$ with $n ⩾ 2$ . We first prove a Sobolev-type inequality with explicit constants for the Laplace operator, which leads to quantitative Carleman-type estimates for holomorphic functions. These results are then extended to holomorphic sections of Hermitian vector bundles satisfying certain curvature restrictions, yielding quantitative versions where previously only non-quantitative forms were available. The proofs refine existing methods through careful constant tracking and by estimating the radius of the uniform sphere condition of the boundary through the Lipschitz constant of its outward unit normal vector.

查看原文本刊更多论文

有界区域上全纯截面的定量carleman型估计

本文建立了C n $\mathbb {C}^n$与n小于2 $n \geqslant 2$中有界域上的厄米向量束的全纯截面的定量carleman型不等式。我们首先证明了拉普拉斯算子的一个带有显式常数的sobolev型不等式，从而得到了全纯函数的定量carleman型估计。然后将这些结果推广到满足某些曲率限制的厄米矢量束的全纯截面，得到以前只有非定量形式可用的定量版本。这些证明改进了现有的方法，通过仔细的常数跟踪和通过其向外单位法向量的Lipschitz常数估计边界的均匀球条件的半径。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.