介于经典型和乘积型的奇异积分算子

摘要

A set of theory of singular integral operators is established, which can be seen as the middle class between the classical single-parameter singular integral operators and the multi-parameter product singular integral operators. The Lp (p > 1 ) boundedness for these operators is obtained, where the L2 boundedness of these operators is obtained by the method of Fourier transform and integration by part and the Lp (p > 1 ) boundedness is obtained by the classical method of Littlewood-Paley-Stein theory.%经典单参数奇异积分算子与多参数乘积型奇异积分算子既有联系也有区别.文中建立一套介于两者之间的奇异积分算子理论,给出该类算子的Lp(p＞1)有界性.其中L2有界性是利用傅里叶变换与分部积分等方法得到的.一般的Lp(p＞1)有界性是利用经典的Littlewood-Paley-Stein理论和方法得到的.