Sharp Estimates of p-Adic Hardy and Hardy-Littlewood-Pólya Operators  

作　　者：Zun Wei FU Qing Yan WU Shan Zhen LU 

机构地区：[1]Department of Mathematics, Linyi University [2]School of Mathematical Sciences, Beijing Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第1期137-150,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.10901076,10931001,11126203and11171345);Natural Science Foundation of Shandong Province(Grant No.ZR2010AL006)

摘　　要：In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.

关 键 词：p-Adic Hardy operator p-Adic Hardy-Littlewood-P61ya operator central BMO function Herz space 

分 类 号：O177[理学—数学]