Lp and BMO Bounds of Weighted Hardy–Littlewood Averages1

This paper characterizes those nonnegative functions ψ defined on 0 1 for which the weighted Hardy–Littlewood average Uψ f → 1 0 f t· ψ t dt is bounded on either Lp n p ∈ 1 ∞ , or BMO n . Meanwhile, the corresponding operator norms are worked out