A new Leray formula for smooth functions on bounded domains in C^n  

作　　者：姚宗元 邱春晖 钟春平 

出　　处：《Science China Mathematics》2002年第5期610-619,共10页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 19771068) ; Mathematical "Tian Yuan" Foundation of China (Grant No. TY10126033).

摘　　要：By means of a new technique of integral representations in C n given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C n , which is different from the well-known Leray formula. This new formula eliminates the term that contains the parameter A from the classical Leray formula, and especially on some domains the uniform estimates for the $\bar \partial - equation$ are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in C n , which are different from the classical ones, when we properly select the vector function W.By means of a new technique of integral representations in Cn given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in Cn, which is different from the well-known Leray formula, This new formula eliminates the term that contains the parameter λ from the classical Leray formula, and especially on some domains the uniform estimates for the -equation are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in Cn, which are different from the classical ones, when we properly select the vector function W.

关 键 词：BOUNDED domain  SMOOTH function  integral representation  LERAY formula  NEW formula. 

分 类 号：O175[理学—数学]