Weighted inequalities for quasilinear integral operators on the semiaxis   and application to the Lorentz spaces
  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. 
Dmitrii V. Prokhorov, Vladimir D. Stepanov
math.FA