Singular Integrals along Submanifolds of Finite Type

摘要

Let n ∈N, n ≥ 2, and y ∈ R~n. Let K(y) be a Calderon-Zygmund kernel, that is, K(y)=Ω(y0Ω/|y|~n, (1.1) Where Ω is homogeneous of degree 0 and satisfies ∫_S~n-1Ω(y)dσ(y)=0. (1.2) Let B(0, 1) denote the unit ball centered at the origin in R~n, let d ∈ N, and let Φ: B(0, 1) → R~d be a C~∞ mapping. Define the singular integral operator T_Φ on R~d by (T_Φf)(x)=p.v.∫_B(0, 1) f(x-Φ(y))K(y)dy. (1.3) The following L~P boundedness theorem can be found in Stein [7].