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THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON stein manifoldS

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Acta Mathematica Scientia 2006年第4期26卷 679-690页

作者：钟同德陈吕萍 School of Mathematical Sciences Xiamen University Xiamen 361005China

Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.

关键词： stein manifold singular integral with Bochner-Martinelli kernel permutation formula regularization problem

UNIFORM ESTIMATES OF SOLUTIONS OF(?)-EQUATION ON stein manifoldS

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Acta Mathematica Scientia 2008年第2期28卷 441-448页

作者：汤冬梅邱春晖钟春平 School of Mathematical Sciences Xiamen University

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a stein manifold, and under suitable conditions gave the solutions of δ^--equation on a stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a stein manifold.

关键词： stein manifold Hermitian metric Chern connection δ^--equation uniform estimate

PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON stein manifoldS

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Acta Mathematica Scientia 2005年第4期25卷 647-657页

作者：陈吕萍林良裕 Department of Mathematics Xiamen University Xiamen 361005 China

Let D be a bounded domain with piecewise C^（1） smooth orientable boundary on stein manifolds, and let Φ（z） be a Cauchy type integral with Bochner-Martinelli kernel Ω（φ^V, S^-, S） and Holder continuous density function φ（ζ）, the authors define a solid angular coefficient α（t） at the point t∈δD, prove that there exist the interior and outer limit values Φ^±（t） under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.

关键词： stein manifold Cauchy type integral Plemelj formula solid angular coefficient

Homotopy formulas and ■-equation on local q-convex domains in stein manifolds

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Science China Mathematics 1997年第8期40卷 817-824页

作者：钟同德 Institute of Mathematics Xiamen UniversityXiamen 361005China

The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in stein manifolds are *** homotopy formulas on local q-convex domains have important applications... 详细信息

关键词： stein manifold Koppelman-Leray-Norguet formula local q-convex domain homotopy formula ■-equation

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in stein manifolds

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Chinese Quarterly Journal of Mathematics 2021年第4期36卷 331-355页

作者： CHEN Shu-jin School of Mathematical Sciences Xiamen UniversityXiamen 361005China

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∂-*** we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.

关键词： ∂-equation Uniform estimation General bounded domain stein manifold Analytic varieties Integral representation

C_(p,q)^(s+α)-forms Solution of _b-equ ation and Its L_(p,q)~s Estimates

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Chinese Quarterly Journal of Mathematics 2003年第3期18卷 234-241页

作者： MA Zhong-tai (Department of Mathematics, China Coal Economic College, Yantai 264005, China) Department of Mathematics China Coal Economic College Yantai 264005

In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form  b-equation on the boundary of pseudoconvex domain in stein manifolds and the L s p,q extimates for the solution.

关键词： inhomogeneous tangential Cauchy-Riemann equations i ntegral representation of  b-solving the kernel of Demaily mand Laurent Thiebaut Chern connection stein manifold L s p,q estim ates