$L^p$ bounds for singular integrals and maximal singular integrals with rough kernels

Abstract

Convolution type Calderón-Zygmund singular integral operators with rough kernels $\pv \Om(x)/|x|^n$ are studied. A condition on $\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p\to L^p$ for $1<p<\nf$ is obtained. This condition is shown to be different from the condition $\Om\in H^1(\sn)$.

Cited by in corpus (3)

• Quantitative weighted estimates for rough singular integrals on homogeneous groups
• $L^p$ estimates and weighted estimates of fractional maximal rough singular integrals on homogeneous groups
• On the composition for rough singular integral operators