Let M+f(x) = sup/l>0(l//i)/^+* (t) denote the one-sided maximal function of Hardy and Littlewood.For w(x) > 0 on R and 1 < p < oo, we show that M+ is bounded on Lp(w) if and only if w satisfies the one-sided A.
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Eric T. Sawyer (1986) studied this question.
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