中文摘要：

利用时频分析方法和Plancherel定理,得到Sobolev空间中小波系与Gabor系各自作成框架的必要条件,从而将L2（R）空间中的结果推广到Sobolev空间中,丰富了Sobolev空间中框架的相关理论.

英文摘要：

By using the time-frequency analysis method and the Plancherel theorem, the author obtained necessary conditions for wavelet and Gabor systems which could be made frames in Sobolev space, respectively. This generalized some results in L2（R ） to Sobolev space, and enriched the related theory about the frames in Sobolev space.