On one Dubinin problem for the weight capacitance of a Hesse condenser with $A_1$-Mackenhaupt weight

For the Hesse condenser in $\mathbb{R}^n$, $n\ge2$, the equivalence of its weight capacitance and its weight modulus with $A_1$-Muckenhoupt weight is proved. This gives a solution of the Dubinin problem on estimating the capacitance of a capacitor with the weight mentioned.