L^{p} BOUNDS FOR SINGULAR INTEGRALS AND MAXIMAL SINGULAR INTEGRALS WITH ROUGH KERNELS

LOUKAS GRAFAKOS ATANAS STEFANOV

Abstract. Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v.Ω(x)/|x|^{n} are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L^{p} → L^{p} for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H^{1}(S^{n−1}).