一类沿曲面的奇异积分算子的L^p－有界性

The L￣P-Boundedness of Some Singular Integral Operators along Surfaces

设ｎ≥３，记∑＿（ｎ－２）是Ｒ￣（ｎ－１）中的单位球面。本文研究了当Ω为Ｒ￣（ｎ－１）上的零次齐次函数，满足消失性条件且Ω∈时，沿某类曲面（ｔ，г（｜ｔ｜））的下列奇异积分算子Ｔｆ（ｘ，ｘ＿ｎ）＝ｐ．ｖ．ｄｔ及其极大算子的Ｌ￣ｐ（Ｒ￣ｎ）－有界性，其中ｂ为有界径向函数，ｘ∈Ｒ￣（ｎ－１），ｘ＿ｎ∈Ｒ且１＜ｐ＜∞．

Let n ≥3, and Σ_(n-2) be the unit sphere in R￣(n-1).In this paper,we prove that if a homogeneous function Ω of degree zero on R￣(n-1) satisfies the cancellation property and Ω ∈ B(Σ_(n-2)),then the following singular integral operators along some surfaces(t,Γ(|t|))and the corresponding maximal operators are L￣P(R￣n)-bounded,where b is a bounded radial functions,x ∈R￣(n-1),x_n ∈R and 1<p<∞.