Investigation of generalized Hardy inequality via a system of nonlinear differential equations in weighted Lebesgue spaces with mixed norm

The main goal of this paper is to found a criteria for two dimensional Hardy operator via a system of nonlinear differential equations in weighted Lebesgue spaces with mixed norm. In particular, it is proved that the weight functions that are the coefficients of a system of nonlinear differential equations are included in the estimate of the two-dimensional Hardy operator in this space.