Estimates of weighted Hardy-Littlewood averages on the p-adic vector space

被引：49

作者：

Rim, Kyung Soo ^{[1
]}

Lee, Jaesung ^{[1
]}

机构：

[1] Sogang Univ, Dept Math, Seoul 121742, South Korea

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 324卷 / 02期

关键词：

p-adic field; p-adic vector space; weighted Hardy-Littlewood averages; BMO;

D O I：

10.1016/j.jmaa.2006.01.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the p-adic vector space Q(p)(n), we characterize those non-negative functions phi defined on Z(p)* = p {w is an element of Q(p): 0 < vertical bar w vertical bar(p) <= 1} for which the weighted Hardy-Littlewood average U phi : f -> integral(Zp)* f(t(.))psi(t)dt is bounded on L-r(Q(p)(n)) (1 <= r <= infinity), and on BMO(Q(p)(n)). Also, in each case, we find the corresponding operator norm parallel to U-psi parallel to. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1470 / 1477

页数：8

共 8 条

[1] RIESZ-POTENTIALS AND EXPLICIT SUMS IN ARITHMETIC [J].