Hausdorff算子在Lorentz空间上的有界性  

The boundedness of Hausdorff operators on the Lorentz space

作　　者：朱相荣[1] 刘宁[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2017年第2期121-126,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11471288;11371136);浙江省自然科学基金资助项目(LYl4A010015)

摘　　要：主要研究了Hausdorff算子在Lorentz空间上的有界性和在L^1空间有界的必要性.通过Fatou引理得出Hausdorff算子在L^1空间有界的必要性;利用Minkowski不等式得到Hausdorff算子在Lorentz空间上有界的充分性条件.It was considered the boundeness of Hausdorff operator on the Lorentz space and the necessary condition on L1 space. By Fatou lemma, the necessity of Hausdorff operator in L^1 space was obtained. The sufficient conditions for the boundedness of Hausdorff operators on Lorentz spaces were obtained by using Minkowski＇s inequality.

关 键 词：Hausdorff算子 LORENTZ空间 MINKOWSKI不等式 FATOU引理 

分 类 号：O174.2[理学—数学]