Abel-poisson type kernel and product type kernel onp-series group

Let G be a p-series group and Ω be a compact subgroup of G. Let λ(x,r) and λⁿ (x,r) be Abelp-poisson type kernel and product type kernel on Ω respectively. In this paper we discuss the approximation properties of such kernels, give the estimates of their moments, obtain the direct and inverse approximation theorems.