Solving the Kerzman’s problem on the sup-norm estimate for \overline{∂} on product domains

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-05-11 DOI:10.1090/tran/9208

Song-Ying Li

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Abstract

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in n n -dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on product domains Ω n \Omega ^n , where Ω \Omega is any bounded domain in C \mathbb {C} with C 1 , α C^{1,\alpha } boundary for some α > 0 \alpha >0 .

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求解乘积域上\overline{∂}的超正值估计的柯兹曼问题

在本文中，作者解决了 Kerzman 提出的一个长期未决问题，即 n n 维复数空间多圆盘上 Cauchy-Riemann 方程的超规范估计。该问题自 1971 年以来一直悬而未决。他还扩展并解决了乘积域 Ω n \Omega ^n 上的问题，其中 Ω \Omega 是 C \mathbb {C} 中的任意有界域，C 1 , α C^{1,\alpha } 边界为某个 α > 0 \alpha >0 。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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