一个判定Hlder条件引理的再推广

A Lemma Futher Being Generalized About Judging Hlder Condition

用一种特别的添辅助项技巧和一系列不等式估计 ,给出奇异积分方程中一个经典引理的再推广及其在广义差商函数和高阶奇异积分中的应用 .这个推广表明 :在曲线上定义的两个函数其中之一不满足 H¨Older条件甚至在曲线上有高阶奇性时 ,其乘积何时满足 H条件 .

In this note,using a special skill to add to auxiliary terms and a series of estimations by inequalities,it is given a further generalization aboat a classical lemma in singular integral equation and applying it to generalized difference quotient function and singular integral of high order.The above generalization shows thatifone of two functions defined in a curve don'tsatisfy H¨Oldercondition,or have even singularities of high order on the curve,under what conditions their product will belong to class H¨O lder.