A new Leray formula for smooth functions on bounded domains in C n |
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Authors: | Zongyuan Yao Chunhui Qiu Chunping Zhong |
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Affiliation: | 1. Department of Mathematics, Xiamen University, 361005, Xiamen, China
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Abstract: | 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. |
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