摘要
H^p(Δ~n)类函数由它的边界函数在正测度集上的限制唯一确定。本文具体指出这类函数能用它的边界函数在正测度集上的积分来表示,我们证明定理设E是T^n上正测度子集,φ_2如文中(7)—(12)式所定义,则对f(z)∈H^p(Δ~n),1<p≤+∞, f(z_1,…,z_n)=lim λ/(2πi)~n integral from n=T^n (φ_2(ξ_1,…,ξ_n)dξ_1…dξ_n)/((ξ_1-z_1)…(ξ_n-z_n)) 且极限是内闭一致收敛的。
It is well known that each function in H^p(⊿~n) is uniquely determined by its boundary function on any positive measured set. In this paper, we give these functions a integral representation by their boundary functions on any positive measured set. We proved the following Theorem. Let E is a positive measured subset on T^n, φ_2 be difined as(7)—(12), then for each f(Z)∈H^p(⊿~n) with 1<p≤+∞, f(z_1,...,z_n)= ■λ/(2πi)~n integral from n=T^n (φ_2(_1…,ξ_n)/((ξ_1-z_1)…(ξ_n-z_n)))dξ_1…dξ_n and the limit is uniform convergence in any compact subset of ⊿~n.
出处
《宁波大学学报（理工版）》
CAS
1989年第1期9-17,共9页
Journal of Ningbo University：Natural Science and Engineering Edition
