We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.
Hardy spaces variable exponents Heisenberg group atomic decomposition Littlewood-Paley characterization