Bounds of weighted Hardy–Cesàro operators on weighted Lebesgue and BMO spaces

摘要

This paper aims to investigate the norms of the weighted Hardy–Cesàro operator U_(ψ,s)f (x) = ∫_0~1f (s(t) ·x)ψ(t) dt on weighted Lebesgue and BMO spaces. Under certain conditions on s(t) and on ω, we characterize the weight function ψ so that U_(ψ,s) is bounded on L~p(ω), BMO(ω). The corresponding operator norms are worked out too. We also give a necessary condition on the weight function ψ, for the boundedness of the commutators of operator U_(ψ,s) on L~p(ω) with symbols in BMO(ω).