Discussion About Some Of The Problems Of The Tb Theorem In The Non-homogeneous Space

In this thesis we mainly discuss several questions resulted from the necessary conditionof Tb-theorem on non-homogeneous spaces: At first we give two kinds of BMO spaceswhich are used in the Tb-theorem. One is a two parameter family of spaces BMO_λ^P(μ).The other is regular BMO space RBMO(μ) In the second_we give the bilinear forms ofCalderon-Zygmund operator T with general kernel which are respectively defined onLipschitz functions and defined for smooth functions. Then we show that the above BMOspaces are equivalent to the Tb-theorem. At last we draw a conclusion that under the sameassumptions Tb₁∈BMO_λ²(μ) implies T_εb₁∈BMO_∧²(μ) (for some∧＞λ) for alltruncated operators with uniform estimates on BMO norms..