General Integral Formulas of (0; q)(q > 0) Differential Forms on the Analytic Varieties

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  • School of Mathematical Sciences, Xiamen University
Chen Shu-jin(1939-), male, native of Fuzhou, Fujian, a Professor (Enjoying the special allowance of the State Council) of Xiamen University, engages in Several Complex Variables

Received date: 2016-03-13

  Online published: 2020-10-20

Abstract

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. 

Cite this article

CHEN Shu-jin . General Integral Formulas of (0; q)(q > 0) Differential Forms on the Analytic Varieties[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(4) : 355 -370 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.04.003

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