H型群上的Hardy-Littlewood-Sobolev不等式和Stein-Wiess不等式  

Hardy-Littlewood-Sobolev inequality and Stein-Wiess inequality on H-type groups

作　　者：胡亭曦[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710129

出　　处：《纺织高校基础科学学报》2013年第2期231-235,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11271299);天元基金资助项目(11126027);陕西省自然科学基础研究计划项目面上项目(2012JM1014)

摘　　要：研究了H型群上一类带权的HLS不等式,也就是所谓Stein-Wiess不等式,并由此得到了H型群上的HLS不等式.通过建立H型群上一类积分算子的Lp-Lq有界性,利用此积分算子与Stein-Wiess不等式的关系,得到所求不等式,从而推广了Heisenberg群上的Stein-Wiess不等式.A Stein-Weiss inequality on H-type groups is studied. By the inequality, the HLS inequality on H-type groups is also derived. By proving the Lp-L estimate of an integral operator, the main result is established based on the relationship between the integral operator and the inequality, and this result im- plies Stein-Weiss inequality on Heisenberg group.

关 键 词：HLS不等式 Stein-Wiess不等式 H型群 

分 类 号：O178[理学—数学]