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

[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.

[发布日期] 2006-12-15

[关键词] p-adic field;p-adic vector space;weighted Hardy-Littlewood averages;BMO