右半圆盘区域上的Hardy空间

Hardy space in half a disc domain

主要通过保形映射进行等价处理的方法对右半圆盘上的Hardy空间进行刻画,得到了右半圆盘Hardy空间的定义、Blaschke乘积、分解定理,对右半圆盘区域上的Hardy空间函数的非切向边界极限进行刻画,并且给出了右半圆盘上的Hardy空间的等价空间,由此对右半圆盘Hardy空间上的有理函数进行刻画,为进一步研究右半圆盘区域上的有理函数逼近提供理论依据.

The Hardy space in the right-half disc in complex plane is studied by conformal mapping.This space is defined in case of 0<p<∞,as a consequence,the Blaschke product and decomposition theorem of this space are obtained.Non-tangential limits of functions of the Hardy space are also defined.Equivalent space of Hardy space in the right-half disc is obtained.A better understanding is now possible about the rational functions defined on the right-half disc.This equivalence provides some theoretical basis to study approximation theory of rational functions on the right-half disc.