沿两类流形上的奇异积分的L^p有界性(英文)

L p Boundedness for Singular Integrals Associated with Two Kind of Manifold

本文讨论了如下奇异积分算子：Ｔｆ（ｘ）＝Ｐ．Ｖ．∫Ｒｎｆ（ｘＰ（ｙ））Ｋ（ｙ）ｄｙ，其中Ｐ（ｙ）＝（ｐ１（ｙ），ｐ２（ｙ），…，ｐｎ（ｙ）），Ｋ（ｙ）＝Ω（ｙ）‖ｙ‖ｎ，∫Ｓｎ１Ω（ｙ）ｄσ（ｙ）＝０．对满足一定条件的Ｐ和Ω∈Ｌｑ（Ｓｎ１）（ｑ＞１）。

In this paper, we consider the following singular integrals:  Tf(x)= P. V. ∫ R n f(x P(y))K(y)dy, where P(y)= γ 1(‖y‖)H 1(y), γ 2(‖y‖)H 2(y), …,γ n(‖y‖)H n(y)), K(y)= Ω(y)‖y‖ n and∫ S n 1 Ω(y)dσ(y)=0. When γ(t)= (γ 1(t), γ 2(t), …,γ n (t)) is highly monotone curve or approximately homogeneous curve and Ω∈L q(S n 1 ) (q> 1), we prove that both T and its maximaloperator T * are bounded on L p(R n), p>1 .