  Analytic capacity is associated with the Cauchy kernel $1/z$ and the
$L^\infty$-norm. For $n\in\mathbb{N}$, one has likewise capacities related to
the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, $1\le i\le 2$,
$x=(x_1,x_2)\in\mathbb{R}^2$. The main result of this paper states that the
capacities associated with the vectorial kernel $(K_1, K_2)$ are comparable to
analytic capacity.
