【摘要】 在经典解析函数边值理论中,当L为复平面上逐段光滑封闭曲线时,在L所围的内部和外部,Cauchy型积分解析;通过对Cauchy主值积分的讨论,可得Cauchy型积分在L上的左、右边值,且边值满足Plemelj公式.基于Koch曲线的构造方法,对一系列Cauchy型积分取极限,并附加上一定的Hlder条件,可得在Koch曲线所围的内部和外部区域内都解析的Cauchy型积分函数,进一步得到与经典解析函数边值问题类似的结果.更多还原

【Abstract】 In this paper,based on the formation of Koch Curve,through discussing the Umit function of a sequence of Cauchy-type integrals,a analytic Cauchy-type integral function was obtained in the interior region and exterior region bounded by Koch Curve attaching some Hldercondition.Furthermore,some similar results was got with the classical boundary value problems for analytic functions.更多还原