Abstract:
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.
Key words:generalized Hardy inequality, nonlinear differential equations, Lebesgue spaces with mixed norm, absolutely continuous function of two variables.
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