Hardy spaces associated with non-negative self-adjoint operators
  Maximal and atomic Hardy spaces Hp and HAp , are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that Hp = HAp with equivalent norms. 
S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev
math.FA