Continuity of Calderón-Zygmund Type Operators on the Predual of a Morrey Space

It is known that the Morrey space is the dual of certain atomic space H ^p,φ . In this paper, we define a notion of a molecule in terms of p and φ and we show that this molecule belongs to H ^p,φ by obtaining a suitable atomic decomposition. We use this result to prove that a Calderón- Zygmund type operator satisfying certain cancelation condition, maps H ^p,φ continuously into itself. By duality, we obtain a continuity result on the Morrey space.