Studies On Real-Variable Bergman Spaces In The Complex Ball

This thesis is devoted to studies on the real-variable Bergman spaces in the complex ball, and it consists of the following three parts:Chapter three is the fist part. First of all, atoms is defined, and we introduce some characters of them. Secondly, we define Lγ,q’,α(Bn) spaces. Then, we introduce real-variable (weighted) Bergman spaces Apα (Bn) of the complex ball in the case0<p≤1with a>-1by using atoms. The real-variable Bergman space Ap,qα(Bn) is defined to be the space of continuous linear functionals f on Lγp,q’,α(Bn) admitting an atomic decomposition, and we prove that Lγp,q’,α(Bn) is the dual space of Ap,qα(Bn)。In the second part, we establish equivalence of Apα(Bn):Ap,qα(Bn)=Ap,∞α(Bn), where a>-1,0<p<1<q<∞and p<q. We prove it by applying the characters of open sets U C Bn. This is the content of the fourth chapter.In the third part, which is the fifth chapter, we present the Marcinkiewicz interpolation theo-rem for operators acting on Apα(Bn) by applying Calderon-Zygmund decompose, as the proof of Marcinkiewicz interpolation theorem for operators acting on Hardy spaces.