Stein流形局部q-凸域上不含边界积分的带权因子的同伦公式

利用权因子,得到了Steln流形局部q-凸域上不含边界积分的(r,s)型微分形式的带权因子的同伦公式及其     

Stein流形局部q-凸域上带权因子的同伦公式和(ē)-方程

本文得到了Stein流形局部q-凸域上(r, S)型微分形式的带权因子的同伦公式及其(ē)-方程的带权因子的解.     

Stein流形q-凸域上的同伦公式和∂-方程

得到了Stein流形局部q-凸域上(r,s)型微分形式的同伦公式和局部q-凸域上(r,s)型(∂)-方程的解,Cⁿ空间的结果是它的特例。这个同伦公式在局部q-凸域上(∂)-方程的一致估计和CR-流形的全纯开拓上有重要应用。     

Stein流形局部q-凸域上带权因子的同伦公式和-方程

本文得到了Ｓｔｅｉｎ流形局部ｑ－凸域上（ｒ，Ｓ）型微分形式的带权因子的同伦公式及其－方程的带权因子的解．     

Stein流形局部q—凸域上带权因子的同伦公式和e↓—方程

本文得到了Ｓｔｅｉｎ流形局部ｑ－凸域上（ｒ,Ｓ）型微分形式的带权因子的同伦公式及其ｅ－方程的带权因子的解。     

复流形上具有非光滑边界的强拟凸域上带权因子的Koppelman-Leray公式

利用权因子,我们得到了复流形上边界不必光滑的强拟凸域上（狆,狇）微分形式的带权因子的Ｋｏｐｐｅｌｍａｎ Ｌｅｒａｙ公式及其 方程的带权因子的解,其特点是不含有边界积分,从而避免了边界积分的复杂估计．其次,引进了权因子,带权因子的积分公式在应用上具有更大的灵活性．     

复流形上的Koppelan－Leray－Norguet公式及其应用

本文得到了复流形上具有逐块光滑边界的有界城Ｄ上的（ｐ，ｑ）型微分形式的Ｋｏｐｐｅｌｍａｎ－Ｌｅｒａｙ－Ｎｏｒｇｕｅｔ公式，在适当假定下得到了Ｄ上方程的连续解．作为应用，得到了Ｓｔｅｉｎ流形上实非退化强拟凸多面体上（ｐ，ｑ）型微分形式的积分表示式以及实非退化强拟凸多面体上方程的连续解．     

复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．     

C~n中具有逐块光滑边界的有界域上带权因子积分表示的拓广式

本文讨论了Cn空间中具有逐块光滑边界的有界域上和强拟凸域上具有拓广的B-M核的(0,q)形式的带权因子的积分表示式,得到了带权因子拓广的Koppelman- Leray-Norguet公式．由此得到了有界域上-方程带权因子的连续解,由于权因子的引入,使得积分公式在应用上(如在函数插值问题的应用)具有更大的灵活性．     

一类解析多面体的奇异积分

本文利用Ｒ．Ｈａｒｖｅｙ和Ｊ．Ｐｏｒｋｉｎｇ的方法首先定义广义式的Ｃａｕｃｈｙ主值，利用同伦公式，借助积分变换技巧研究Ｗｅｉｌ型积分的边界性质，得到Ｐｌｅｍｅｌｊ公式．它有别于通常研究边界性质的方法．本文引入细复广义权和Ｃｈｏｑｕｅｔ型复广义权的概念，讨论了某些与复广义权相关的函数的拟连续性与细拟处处连续的关系．     

WEIGHTED KOPPELMAN－LERAY－NORGUET FORMULAS ON A LOCAL q－CONCAVE WEDGE IN A COMPLEX MANIFOLD

A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula with-out boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local q-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the intervolation of functions.     

A NEW FORMULA WITHOUT BOUNDARY INTEGRALS ON A STEIN MANIFOLD

A new Koppelman-Leray-Norguet formula of (p-1,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of (?)-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.     

Homotopy formulas and\bar \partial -equation on localq-convex domains in Stein manifolds-equation on localq-convex domains in Stein manifolds

The homotopy formulas of (r, s) differential forms and the solution of $\bar \partial $ -equation of type (r, s) on localq-convex domains in Stein manifolds are obtained. The homotopy formulas on localq-convex domains have important applications in uniform estimates of $\bar \partial $ -equation and holomorphic extension of CR-manifolds.     

在解析簇上(0,q),(q>0)微分形式的一般积分公式（英文）

In this paper, firstly using different method and technique we derive the corresponding integral representation formulas of(0, q)(q 0) differential forms for the two types of the bounded domains in complex submanifolds with codimension-m. Secondly we obtain the unified integral representation formulas of(0, q)(q 0) differential forms for the general bounded domain in complex submanifold with codimension-m, which include Hatziafratis formula, i.e. Koppelman type integral formula for the bounded domain with smooth boundary in analytic varieties. In particular, when m = 0, we obtain the unified integral representation formulas of(0, q)(q 0) differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.     

HOMOTOPY FORMULA FOR A LOCAL q-CONCAVE WEDGE IN STEIN MANIFOLDS AND IT'S APPLICATIONS

1IntroductionTheauthorhasobtainedaKoppelman-Leray-Norguetformulaforaiccafq-coneavewedgeinndimensionalSteinmanifoldsX[11,inthispaperbasedonthisformulaweobtainahomotopyformulaforalocalq-concavewedge,byusingthisformulaweobtainthesolutionformulafor0-equationonlocalq-concavewedges,anddiscussanextensionproblemonlocalq-concavewedges.Inviewofsavespareweusethenotationsdefinitionsandresultsdirectlywithoutspreadout.airlateruseweonlyintroducetwonewdefinitions[2]:Definition1.1Acolloction(U,pl,''tPN)wi…     

Integral representation formulas for differential forms on complex manifolds and applications to the 327-01327-01327-01-equation

Summary An explicit Koppelman-Leray-Norguet type integral formula for differential forms is derived on generalized analytic polyhedra on complex manifolds which arise as analytic subvarieties of domains ofC ⁿ. Using this formula we give an explicit solution operator to the -equation on strictly pseudoconvex polyhedra in that setting and we prove that this solution operator admits uniform estimates.     

Stein流形上(p,q)型Koppelman-Leray-Norguet公式

设M是复n维Stein流形;并设开集D??M具有逐块C¹边界.本文利用陈度量和陈联络,把Stein流形上(0,q)形式的Koppelman-Leray-Norguet公式推广到(p,q)形式,并得到D上?-方程的解.最后,还给出了Stein流形上实非退化强拟凸多面体的Koppelman-Leray-Norguet公式及其?-方程的解.