Abstract
The criteria for the fulfillment of continuous and discrete inequalities involving Hardy operators are one of the key problems in the theory of weighted inequalities. The study of discrete inequalities for the class of matrix operators can be considered a new direction of research. In general, since the stability criterion in the weighted Lebesgue space for a discrete operator with a matrix kernel is not defined, various conditions are imposed on the matrix, which allows for obtaining broader results compared to the case without a matrix. In this work, we consider discrete quasilinear operators with matrices satisfying certain conditions. The results obtained for quasilinear inequalities can be applied to the description of bilinear Hardy inequalities.