四元数分析中的高阶奇异积分

High Order Singular Integrals in Quaternion Analysis

借助于Hadamard关于高阶奇异积分有限部分的思想,研究关于四元数分析中五类拟Bochner-Marti-nelli型高阶奇异积分的归纳定义,讨论了它们的Hadamard主值的递推公式、计算公式和各种微分公式.在证明了这五种拟B-M型高阶奇异积分的Hlder连续性的基础上,还得到了其各种微分的Hlder连续性.

By using the Hadamard＇s idea for principal value of high order singular integrals, this paper explores the induction definition for five kinds quasi Bochner - Martinelli type high order singular integrals in Quaternion analysis, and discusses recurrence formula, computation formula, and differential formula of the Hadamard principal value for them. The HSlder continuity for them and their differentions are all obtained.