𝐿^{𝑝} bounds for the commutators of singular integrals and maximal singular integrals with rough kernels

Abstract

The commutator of convolution type Calderon-Zygmund singular integral operators with rough kernels p . v . Ω ( x ) | x | n p.v. \frac {\Omega (x)}{|x|^n} are studied. The authors established the L p ( 1 > p > ∞ ) L^p\,(1>p>\infty ) boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition Ω ∈ H 1 ( S n − 1 ) . \Omega \in H^1(S^{n-1}).