一类沿曲面的奇异积分算子

A claSS of Singular Integral Operators along Surfaces

记Σ＿（ｎ－２）为ＩＲ￣（ｎ－１）中的单位球面。本文证明了当Ω为ＩＲ￣（ｎ－１）上的零次齐次函数，满足消失性条件，及时，沿任意曲面（ｔ，Г（｜ｔ｜））的主值奇异积分算子及其极大算子在Ｌ￣２（ＩＲ￣ｎ）上是有界的，此处ｂ为ＩＲ￣（ｎ－１）上的有界径向函数，ｘ∈ＩＲ￣（ｎ－１），ｘ＿ｎ∈ＩＲ。

Let Ω be an homogeneous function of degree zero on R￣n-1,and Ω satisfy the can-cellation. It is proved in this paper that a class of singular integral operators along arbitrarysurfaces are bounded on L￣2(R￣n) provided Ω belongs to certain space generated dy blocks, wherethe kernels of these operators take the form of b(t)Ω(t)/|t|￣n-1, and b is a bounded radial functionon R￣n-1.