L^p bounds for singular integrals and maximal singular integrals with rough kernels
Loukas Grafakos and Atanas Stefanov
Convolution type Calderón-Zygmund singular integral operators with rough kernels p. v. $\Omega(x)/|x|^n$ are studied. A condition on $\Omega$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \to L^p$ for $1 \lt p \lt \infty$ is obtained. This condition is shown to be different from the condition $\Omega\in H^1({\mathbf S^{n-1}})$.