在 Stein 流形中有界域的解析簇上积分表示及其应用

doi:10.13371/j.cnki.chin.q.j.m.2021.04.001

数学季刊 ›› 2021, Vol. 36 ›› Issue (4): 331-355.doi: 10.13371/j.cnki.chin.q.j.m.2021.04.001

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在 Stein 流形中有界域的解析簇上积分表示及其应用

School of Mathematical Sciences, Xiamen University

收稿日期:2021-06-21 出版日期:2021-12-30 发布日期:2021-12-30
作者简介: CHEN Shu-jin (1939-), male, native of Fuzhou, Fujian, professor (enjoying the special allowance of the State Council) of Xiamen University, engages in several complex variables.

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds

School of Mathematical Sciences, Xiamen University

Received:2021-06-21 Online:2021-12-30 Published:2021-12-30
About author: CHEN Shu-jin (1939-), male, native of Fuzhou, Fujian, professor (enjoying the special allowance of the State Council) of Xiamen University, engages in several complex variables.

摘要/Abstract

摘要：

In this paper, we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds (the two types bounded domains in [3] are regarded as its special cases). Secondly we get the integral formulas of the solution of \overline \partial-equationequation. And we use a new and unique method to give a uniform estimate of the solution of \overline \partial-equation, which is different from Henkin’s method.

关键词: \overline \partial-equationequation, Uniform estimation, General bounded domain, Stein manifold, Analytic varieties, Integral representation

Abstract:

In this paper, we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds (the two types bounded domains in [3] are regarded as its special cases). Secondly we get the integral formulas of the solution of \overline \partial-equation. And we use a new and unique method to give a uniform estimate of the solution of \overline \partial-equation, which is different from Henkin’s method.

Key words: \overline \partial-equation, Uniform estimation, General bounded domain, Stein manifold, Analytic varieties, Integral representation

中图分类号:

O174.56

陈叔瑾. 在 Stein 流形中有界域的解析簇上积分表示及其应用[J]. 数学季刊, 2021, 36(4): 331-355.

CHEN Shu-jin. The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(4): 331-355.

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在 Stein 流形中有界域的解析簇上积分表示及其应用

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds

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