Li Hong CUI(1),Qi Xiang YANG(2
Q spaces (or Qp, or Qα spaces), are studied heavily by many authors. In particular, Wu and Xie generalized Q spaces to the Qpα,q spaces in recently. In this paper, we show first the equivalence of some real variable characterization and wavelet characterization for general Q spaces. Our main idea is to use In dimensional wavelet to analyze the elements in Qpα,q on Rn. Furthermore, we construct the pre-dual spaces Ppα,q of Qpα'q, where Ppα,q are generated by atoms which are denned by wavelets.