Abstract
This paper aims to investigate the boundedness of the p-adic analog of the weighted Hardy–Cesàro operator Uψ,s:f→∫Zp⋆f(s(t)⋅)ψ(t)dt on weighted Lebesgue spaces and weighted BMO spaces. In each case, we obtain the corresponding operator norms |Uψ,s|. In particular, these results have a surprising relevance to discrete Hardy inequalities on the real field. We prove a reverse BMO–Hardy inequality and give a necessary condition on ψ so that the commutator of Uψ,s is bounded on Lωr(Qpn) with symbols in BMOω(Qpn).
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