A Kind of Integral Representation on Complex Manifold  

作　　者：Teqing Chen Zhiwei Li 

机构地区：[1]School of Information Management,Minnan University of Science and Technology,Shishi 362700,China [2]School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou 362000,China

出　　处：《Journal of Mathematical Study》2022年第1期95-108,共14页数学研究（英文）

基　　金：supported by Educational and Scientific Research Funding Program for young and middle-aged teachers in Fujian Province,China(Grant No.JT180700).

摘　　要：In this paper,by using the Hermitian metric and Chern connection,we study the case of a strictly pseudoconvex domain G with non-smooth boundaries in a complex manifold.By constructing a new integral kernel,we obtain a new Koppelman–Leray–Norguet formula of type(p,q)on G,and get the continuous solutions of¯∂–equations on G under a suitable condition.The new formula doesn’t involve integrals on the boundary,thus one can avoid complex estimations of the boundary integrals,and the density of integral may be not defined on the boundary but only in the domain.As some applications,we discuss the Koppelman–Leray–Norguet formula of type(p,q)for general strictly pseudoconvex polyhedrons(unnecessarily non-degenerate)on Stein manifolds,also get the continuous solutions of¯∂–equations under a suitable condition.

关 键 词：Complex manifold strictly pseudoconvex domain non-smooth boundary Koppelman–Leray–Norguet formula ∂–equation 

分 类 号：O17[理学—数学]