摘要
在C^d中,由函数g(z)=∑_(n=0)~∞a_nz^n(a_n≥0)生成的解析Hilbert空间H_d^g(B_d^(R^(1/2)))是酉不变的再生核Hilbert空间.本文证明了,当d≥2时,若sup{a_nR^n}<+∞,则有球代数A(B-2^(R^(1/2)))中的函数f(?)M,即H_d^g(B_d^(R^(1/2)))上的乘子代数M是H~∞(B_d^(R^(1/2)))的真子集.由此可知,若存在M>0,使得0≤a_0≤a_1≤…≤M,n=0,1,2,…,则H_d^g(B_d^(R^(1/2)))不是次正规的.因而不存在C^d中的正测度μ,使得对任何f∈H_d^g(B_d^(1/2))(?)而且在H_d^g(B_d^(1/2))上的von Neumann不等式不成立.
Let Bd be the unit ball ofd-dimensional complex Euclid space C^d, H^9d（Bd√R） the reproducing kernel Hilbert space with u-invariant reproducing kernel K（z, w） = 9（（z,w）, where g（z）=∑^∞n=0anz^n（an≥0） is the generating function of the space H^9d（Bd√R） In this paper, we show that the multiplier algebra of the spaceH^9d（Bd√R） a proper subset of H∞（Bd√R）, and there exists a holomorphic self-mapping w from Bd into Bd√R such that the multiplication operator Mwis not bounded when the {an}^∞n=0is bounded andd ≥ 2. Frthermore, we prove that if the coefficients sequence {an}^∞n=0 of the generating function g is a bounded, non-decreasing sequence, i.e. there exists a positive number M such that 0≤a0〈al ≤...≤M, n=0,1,2,..., H^9d（Bd√R） then the space H^9d（Bd√R） is not subnormal, in other words, there is not any positive measure μ on C^d such that‖f‖^2H^9d=∫Cd│f（z）│^2dμ（z）M for each fεH^9d（Bd√R） and then von Neumann＇s inequality does not hold on the space H^9d（Bd√R）
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2014年第2期249-260,共12页
Acta Mathematica Sinica：Chinese Series
基金
浙江省自然科学基金资助项目(Y6110824)
浙江省重点学科"基础数学"建设经费资助项目
