Predual spaces for Q spaces

To find the predual spaces Pα(Rn) of Qα(Rn) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderón-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn).