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Characterizations are obtained for those pairs of weight functions w, v for which the Hardy operator Tf(x) = /¿v f(s) ds is bounded from the Lorentz space L"((0,oo), vdx) to Lpi((0,oo),wdx), 0 <p, q, r,s < oo. The modified Hardy operators Tnf(x) = x"'Tf(x) for tj real are also treated.doi:10.1090/s0002-9947-1984-0719673-4 fatcat:mfyojzdqjrftzgmtpg2ig3kvnm