无界区域上Cauchy型奇异积分算子的性质

Some Properties of Cauchy-type Singular Integral Operator on Unbounded Domains

中文关键词:  正则函数  Cauchy型奇异积分算子  无界区域  H\"{o}lder连续.

英文关键词:regular function  Cauchy-type singular integral operator  unbounded domains  H\"{o}lder continuity.

中文摘要:

      在修正的Cauchy核的基础上, 我们研究了正则函数相应的无界区域上Cauchy型奇异积分算子在三种情况下的H\"{o}lder连续性: (1)两点都在区域的边界上; (2)一点在区域的边界上, 另一点在区域的内部(外部); (3)两点都在区域的内部(外部).

英文摘要:

      On the basis of introducing the modified Cauchy kernel, we discuss the H\"{o}lder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases: two points are on the boundary of region; one point is on the boundary and another point is in the interior(or exterior) of the region; two points are in the interior (or exterior) of the region.