非整数阶高阶奇异积分的微分公式

On the Differential Formulas for Singular Integrals of High Non-Integral Order

在核密度有足够高阶的导数类（而不必在相应Ｈｏｌｄｅｒ函数类），给出非整数阶高阶奇异积分的连续性和微分公式．这些结果本身以及为今后导出非整数阶高阶奇异积分的换序公式（另文）有重要意义．在证明方法上与整数阶高阶奇异积分时的相应情形颇多不同．

When kerncl density is in the class of continuous function to possessing sufficient derivative of high order (and needn' t in the class of corresponding Holder function), in this paper it is given the continuity and the differential formulas for singular integrals of high non-integral order. The above results themselves and in order to prove in future the formulas to changing order of integration for singular integrals of high non-integral order(another paper) will have important significance. The method to prove in this paper is more different from the method in the corresponding cass of singular integrals of high integral order.