H^(1/2)空间上的有界线性泛函

BOUNDED LINEAR FUNCTIONALS ON H^(1/2) SPACE

讨论了H'空间上有界线性泛函的各种表示之间的关系,并在此基础上获得了H^(1/2)上有界线性泛函之集(H^(1/2))~*与A_1={g|g∈H(Δ)且|g(z_1)—g(z_2)|≤K|z_1—z_2|,z_1,z_2∈Δ}的——对应关系,其中Δ表示单位圆盘,H(Δ)表示在Δ内的解析函数之集。

In this paper we discuss the relations between the representations of bounded linear functionals on H' spaces. Furthermore, we obtain one-to-one correspondence of the set (H^(1/2))' = {φ|φis a bounded linear functional on H^(1/2)} and the set A_1={g|g∈H(Δ), and |g(z_1)—g(z_2)|≤K|z_1—z_2|, z_1, z_2∈Δ}, whereg ∈ H(Δ)if g is aanalytic function on unit disc Δ.