摘要
设(Ω,μ)是一个概率空间,φ是一个Musielak-Orlicz函数且设q>1.在这篇文章中,作者建立了广义Orlicz-Lorentz空间上的H?lder不等式.特别地,在A_(∞)权条件下,作者证明了加权Lorentz空间上的Holder不等式.更进一步,这篇文章也得到了Orlicz-Lorentz空间上的Holder不等式.但是,该结果不需要Musielak-Orlicz函数上的相应假设,仅仅需要增长性条件.
Let(Ω,μ)be a measure space.Assumeφ:Ω×[0,∞)→[0,∞)is a Musielak-Orlicz function and q∈(1,∞).In this paper,we establish the Holder inequality for the generalized Orlicz-Lorentz spaces L^(φ,q)(Ω).Especially,under the A_(∞)weighted condition,we show that the Holder inequality holds true in weighted Lorentz spaces.Furthermore,the Holder inequality for Orlicz-Lorentz spaces we obtained does not need any of those assumptions in Musielak-Orlicz setting.Only growth conditions are assumed.
作者
谢广亨
Xie Guangheng(School of Mathematics and Statistics,Central South University,Changsha,Hunan 410083,China)
出处
《数学理论与应用》
2020年第2期104-117,共14页
Mathematical Theory and Applications
基金
supported by China Postdoctoral Science Foundation(Grant No.2019M662797)
