Abstract:

The bilinear forms of Calderón-Zygmund operator T with Tb-theorem on non-homogeneous spaces which is defined on smooth functions are introduced. Under such condition, the necessity of Tb-theorem has been proved and the two BMO spaces are equivalent to the Tb-theorem on non-homogeneous spaces have been shown.

Key words: non-homogeneous space; Calderón-Zygmund operator; Tb-theorem; bilinear form; smooth function