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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
In this paper, we define the abstract Hardy spaces.And then we propose some general conditions which guaranteethe continuity from our Hardy space into $L^1$. At last,we give the definition of the ${
m BMO}$ space and studythe relationship between abstract Hardy spaces and ${
m BMO}$ space.