Abstract
The optimal sucient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces deÞned on homogeneous groups. In some particular case the found conditions are necessary for the cor- responding inequalities to be valid. Also, the necessary and sucient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces deÞned on homogeneous groups.
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