加权Hardy空间中函数的积分表示

The integration of functions in the weighted Hardy spaces

主要对管状区域上加权Hardy空间H(s)(ψ,Γ)中的解析函数进行了刻画.证明了F(z)∈H^(s)(ψ,Γ)(2s>n),当且仅当F(z)可以表示为一个支集在U(ψ,Γ)上的Ls'^2(Rn)中函数的Fourier-Laplace变换.借助于Paley-Wiener定理,给出了当s=1时,H^(1)(ψ,Γ)空间中解析函数F(z)与其1阶偏导数∂F(z)/∂zk(k=1,2,…,n)的频谱函数之间的等式关系.

Analytic functions in Hardy space H^(s)(ψ,Γ)on tube domains are described.We prove that F(z)∈H^(s)(ψ,Γ)(2s>n)if and only if F(z)can be expressed as Fourier-Laplace transform of a function belonging to Ls'^2(R^n)and is supported in set U(ψ,Γ).With s=1,relationships between spectral functions of F(z)in H^(1)(ψ,Γ)and its partial derivatives of one order ∂F(z)/∂zk for kequalsto1,2,…,n.