In this paper a two weight criterion for multidimensional geometric mean operator in variable exponent Lebesgue space is proved. Also, we found a criterion on weight functions expressing one-dimensional Hardy inequality via a certain nonlinear differential equation. In particular, considered nonlinear differential equation is nonlinear integro-differential equation.
Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type
Two-dimensional Systems that Arise from the Noether Classification of Lagrangians on the Line
Searching optimal shapes for blades of a fan
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