核密度具有可数个第一类间断点的Cauchy型积分

核密度具有可数个第一类间断点的Cauchy型积分 The Cauchy Type Integrals with Numerable Discontinuous Points of the First Kind in the Kernel Function 吴和林 WU He-lin 1 2 first-author 杜金元 DU Jin-yuan 1 2 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 当在单位圆周上核密度函数为具有可数个第一类间断点A={ak}+∞k=1的H0,μ类函数时证明了其Cauchy型积分的收敛性.在A的聚点a0附近得出的结果是:当z从上半单位圆内绕过由可数个圆构成的测度可任意小的集合趋近a0时,Cauchy型积分满足μ阶H lder条件. In this paper,the Cauchy-type integrals with H 0,μ kind kernel function which has numerable discontinuous points of the first kind A={a k } +∞ k=1 is considered.We mainly study its properties arround a 0 ,the limiting point of {a k } +∞ k=1 .The result is the Cauchy-type integrals satisfies H μ condition when z tends to a 0 going around a set of numerous disjointed sets whose measure can be arbitrary small. Cauchy型积分 Hlder连续性 H0 μ类函数 O172.2 国家自然科学基金资助项目（19971064） 2004-05-01 2021-04-01 5