This is an announcement for the paper “Weighted inequalities for quasilinear integral operators on the semiaxis and application to the Lorentz spaces” by Dmitrii V. Prokhorov and Vladimir D. Stepanov. Abstract: Weighted $L_p-L_r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the Lorentz $\Gamma$−spaces is given. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04884