振荡奇异积分的一个权模不等式(英文)

A Weighted Norm Inequality for Oscillatory Singular Integrals

本文证明：对于带多项式相函数的振荡奇异积分算子，权模不等式∫Ｒｎ｜Ｔｆ（ｘ）｜ｐｗ（ｘ）ｄｘＣ∫Ｒｎ｜ｆ（ｘ）｜ｐＭ［ｐ］＋１ｗ（ｘ）ｄｘ，１＜ｐ＜∞成立，其中ｗ是非负局部可积的权函数，Ｍｋ表示Ｈａｒｄｙ－Ｌｉｔｌｅｗｏｏｄ极大算子的ｋ次迭代。

In this paper, we show that the weightes norm inequality  ∫ R n |Tf(x)| pw(x)dxC∫ R n |f(x)| pM +1 w(x) dx, 1<p<∞,  holds for oscillatory singular integral operators with polynomial phases, where M is the Hardy Littlewood maximal operator and M k is M iterated k times, is the integer part of p .