Koppelman-Leray Norguet Formulas With Weight Factors And Estimates For Solutions With Weight Factors Of (?)-Equations On Stein Manifolds

The integral representation method of several complex variables is one of main methods of complex analysis in several variables,because one of its main virtues is that it is easy to estimate as the Cauchy integral formula in one complex variable.In this paper,by means of the ideas of Demailly and Laurent-Thiebaut and the Hermitian metric and Chern connection,by introducing the weight factors,we obtain the weighted Koppelman-Leray-Norguet formula on strictly pseudoconvex domains with piecewise C~1 smooth boundaries on Stein manifolds.Since the weight factors are introduced,the weighted integral formulas have much freedom in applications such as in the interpolation of functions. By means of the trick of Range and Siu,the author obtains the uniform estimates of the solutions with weight factors of(?)-equations on strictly pseudoconvex domains with piecewise C~1 smoooth boundaries on Stein manifolds.The whole dissertation includes three chapters:In the first chapter,the author introduces some definitions,the basic lemmas and notations on Stein manifolds.In the second chapter,by means of the ideas of Demailly and Laurent-Thiebaut, and the Hermitian metric and Chern connection,by introducing the weight factors,the Koppelman-Leray-Norguet formula with weight factors on strictly pseudoconvex domains with pieccwise C~1 smooth boundaries on Stein manifolds is obtained.Since the weight factors are introduced,the weighted integral formulas have much freedom in applications such as in the interpolation of functions.In the third chapter,by means of the trick of Range and Siu,the uniform estimate of solution with weight factors of(?)-equations on strictly pseudoconvex domains with piecewise C~1 smoooth boundaries on Stein manifolds is given.