推广的Q空间

Notes on Generalized Q Spaces

Q空间(或Qp,或Qα空间)的研究受到许多研究者的关注.最近,Wu和Xie将Q空间推广到Qpα,q空间.本文对一般的Q空间进行研究.首先,表明某些实变量刻画和小波刻画的等价性,主要想法是用2n维小波分析属于n维空间Rn的Qpα,q中的元素.其次,也构造出了空间Qpα,q的预对偶空间Ppα,q,其中Ppα,q是由小波定义的原子生成.

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.