Clifford分析中超正则函数的拟Cauchy型奇异积分算子的换序公式

Transformation formula of Cauchy type singular integral operators with a weakly singular integral operators in Clifford analysis

研究了Clifford分析中弱奇异积分算子和以弱奇异积分算子的奇点为积分变量的带参量的Cauchy型奇异积分算子在Liapunov闭曲面上的换序问题.首先证明了相关的奇异积分的性质,并利用这些性质证明了两个累次积分是有意义的,然后将积分区域分为几部分,从而将积分算子分为带有奇性的部分和不带奇性的部分.证明了带有奇性的部分的极限是零,不带奇性的部分相等.这样就证明了弱奇异积分算子和以弱奇异积分算子的奇点为积分变量的Clifford分析中超正则函数的拟Cauchy型奇异积分算子的换序公式.

It studies the transformation problem of a weakly singular integral with the Cauchy type singular operators whose singular point is the integral variable of the weakly singular integral on Liapunov closed surface in Clifford analysis. Firstly, it proves the nature of relevant singular integrals and then it proves that the two iterated integrals are well defined by using that nature. Next, it divides the integral domain into several parts. Naturally, the integral operators are grouped into two parts.One is with the singular integrals and the other is with non-singular operators, and it proves that the limit of the part with the singular operator is operators is zero and the part without singularity are equal. Thus, it proves the transformation formula of a weakly singular integral with the Cauchy type singular operators whose singular point is the integral variable of the weakly singular integral.