Pointwise convergence of singular convolution operators (Q789662)

D. Geller and E. M. Stein have defined singular convolution operators on the Heisenberg group, and have proved \(L_ p\)-continuity and \(L_ p\)- convergence of the truncated kernels. The author shows in this paper that the maximal operator associated with the truncations maps \(L_ p\) to \(L_ p\) for \(1<p<\infty\), and hence gets almost everywhere convergence for the truncated transforms.