Cauchy－Riemann方程的C_（p，q）^（k＋α）－型算子解

THE OPERATOR SOLUTIONS OF C_(p,q)￣(k+α)-FORMS FOR THE CAUCHY-RIEMANN EQUATIONS

研究对给定在Ｃｎ中拟凸域上的Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的Ｃ∞类（ｐ，ｑ）型微分形式解，不仅证明了严格拟凸域上Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的Ｃｋ类（ｐ，ｑ）型微分形式解，而且给出了其方程在Ｃｎ中有界开集上的Ｃ＿（ｐ，ｑ）￣（Ｋ＋ａ）型（ｐ，ｑ）微分形式解，推广了Ｂｏｎｎｅａｎ和Ｄｉｅｄｅｒｉｃｈ最近所得到的结果．

In this paper the(p,q) differential forms solution with class C∞ of a pseudoconvex domain in Cnfor Cauchy-Riemann equation is discussed and, not only the(p,q) differential forms solution with class Ck for the Cauchy-Riemann equation is proved and, as a generalization of the recent result of Bonnean and Diederich, the (p,q) differential forms solution with class C(p,q)(k+a) of the equations on an bounded open set in Cn is also obtained.