Equivalent Characterizations of Hardy Spaces

Abstract:

      Let G be the (2n+1) dimensional Heisenberg group over a local field K. In this paper we prove the equivalence of Hardy spaces defined by some kinds of maximal functions and give the atomic decomposition of Hardy spaces. Applying these equivalent definitions and some convolution operator theorems, we characterize Hardy spaces by square functions Luzin area functions and Littlewood Paley functions.