Generalized Calderón-Zygmund operators on homogeneous groups and applications

There are two folds of this article. The first part is concentrating on estimates for generalized Calderón-Zygmund operators acting on Hardy spaces H ^p (G). Here G is a simply connected homogeneous Lie group. We also obtained estimates on the spaces L ^∞ (G) and BMO ^p (G). The second part of this article is applications of results from the first part to the (Formula presented.) -Neumann problem on bounded, smoothly pseudoconvex domains in C ⁿ⁺¹ . We obtain H ^p estimates for the Calderón operator when G = H _n , the n-dimensional Heisenberg group.