The spaces can be characterized by smooth functions. It is a well known work from some mathematicians.There is a strong relation between Soblev space and Besov space. Sobolev spaces was introduced by Russian mathematician Sergei Sobolev in 1930s. His creating space has great application for analyzing of solution of ordinal differential equations and partial differential equations. According to above the applications, we had had natural question of how to characterize of the space by space of classical functions. However, in 1964 year, we had a partial answer of that from working of Meyers and Serrin.