Uniform Estimates Of Solutions With Weight Factors Of (?)-Equations On Local Q-Convex Wedges In C~n

C.Laurent-Thiebaut & J.Leiterer studied local q-convex wedges in C~n,which are extensions of piecewise smooth pseudoconvex domains,obtained the homotopy formula and the uniform estimates for the Cauchy-Riemann equation on q-convex wedges in C~n.By means of the ideas of C.Laurent-Thiebaut & J.Leiterer,the author obtains the homotopy formula with weight factors and uniform estimates of the solutions with weight factors of (?)-equations on local q-convex wedges in C~n.The whole dissertation includes four chapters.The aim of this paper is to generalize the uniform estimates of solutions of(?)-equations to the uniform estimates of solutions with weight factors of(?)-equations on local q-convex wedges in C~n.In the first chapter,the author introduces some definitions,the basic lemma and notations,constructs the integral kernel with weight factors. In the second chapter,the local q-convex wedges in C~n are defined.A Leray map is given.In the third chapter,we obtains a weighted Koppelman-Leray-Norguet formulas and solutions with weight factors of(?)-equation on local q-convex wedges in C~n.We construct a new integral kernel with weight factors of local q-convex wedges without boundary.Then we get a new homotopy formula with weight factors and solutions with weight factors of(?)-equation.Firstly,the new weighted formula does not involve boundary integrals,and is especially suitable for the case of the local q-convex wedge with a non -smooth boundary,so one can avoid complex estimates of boundary integrals.and the desity of integral may be not defined on the boundary but only in the domain.Secondly,since the weight factors are introduced,the weighted integral formulas have much freedom in applications such as the interpolation of functions.Finally,a local q-convex wedges in C~n is an extension of piecewise smooth pseudoconvex domain.so the homotopy formular with weight factors has its generalization meaning,it has important applications in uniform estimates of solution with weight factors of(?)-equation and holomophic externsion of CR-manifolds.In the fourth chapter,by means of the ideas of C.Laurent-Thiebaut & J.Leiterer,the author first admits some estimate of the integral operator H for(n,r)(r＞0) differential forms on local q-convex wedges in C~n.Then by means of the trick of Range-Siu trick the author complicatedly calculates the uniform estimates of solutions of(?)-equation on local q-convex wedges in C~n.