Ling-Xiao Zhang

Sharp boundedness criteria for nonnegative kernels on regular curves in the Heisenberg group

In this paper we study singular integrals associated with the nonnegative kernels \[ K_\alpha(x,y,z)=\frac{|z|^{\alpha/2}}{\|(x,y,z)\|^{\alpha+1}}, \qquad \alpha>0, \] in the first Heisenberg group $\mathbb H$, where $\|\cdot\|$ denotes the Kor\'anyi norm. This family was introduced by Chousionis and Li. We first show...