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

In the p-adic vector space Qn p, we characterize those non-negative functions ψ defined on Z∗p = {w ∈ Qp: 0 < |w|p 1} for which the weighted Hardy–Littlewood average Uψ : f → Z∗p f (t ·)ψ(t) dt is bounded on Lr (Qn p) (1 r ∞), and on BMO(Qn p). Also, in each case, we find the corresponding operator norm Uψ . © 2006 Elsevier Inc. All rights reserved