【摘要】 目的研究Ba空间和Orlicz空间中推广的Hardy-Hilbert不等式。方法借助有界线性算子理论,将Orlicz空间作为特殊的Ba空间来看待。结果首先建立了Ba空间中的Hardy-Hilbert不等式,然后,作为推论给出满足Δ2∩EF条件的Orlicz空间中的如下Hardy-Hilbert不等式:∫0+∫∞0+∞(f(x)g(y)/x+y)dxdy≤c‖f‖M‖g‖(N),f∈LM*,g∈LN*,∑∞m,n=1(ambn/m+n)≤c‖a‖M‖b‖(N),a∈LN*,b∈lN*。结论文中的讨论方法说明作为一种具体的Banach空间,Ba空间不仅为研究函数逼近理论、算子内插理论和调和分析理论提供了典型的验证空间,而且其本身也是空间理论中处理问题的一种方法。更多还原

【Abstract】 Aim The Hardy-Hilbert inequality is extended in Ba space and Orlicz space.Methods By dint of bounded linear operator theory,the Orlicz space is regarded as particular Ba space.Results A kind of Hardy-Hilbert inequality is established in Ba space.As a corollary,the generalized Hardy-Hilbert inequality which satisfies Δ2∩EF in Orlicz space is given as follows: ∫+∞0(f(x)g(y)/x+y)dxdy≤c‖f‖M‖g‖(N),f∈L*M,g∈L*N,∑∞m,n=1(ambn/m+n)≤c‖a‖M‖b‖(N),a∈L*N,b∈l*NConclusion The discussion in this paper shows that Ba space theory is not only a typical validation space of the function approximation theory,the operator interpolation theory as well as harmonic analysis theory,but also a way of tackling with issues concerning theories on space.更多还原