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In this paper,the conditions on pairs of weights(u,v)are given such that for the generalized Hardy operator Tf(x)=∫0^∞K（x,y)f(y)dy the following Φ-inequality holds:Φ2^-1(∫0^∞Φ2（Tf(x))V(x)dx≤CΦ1^-1(∫0^∞Φ1(f(x))U(x)dx)，where Φ1,Φ2 are Young function;the cor