Capacities associated with scalar signed Riesz kernels, and analytic capacity Joan MateuLaura PratJoan Verdera 42B20analytic capacityscalar signed Riesz kernelslinear growth Analytic capacity is associated with the Cauchy kernel $1/z$ and the space $L^{\infty}$. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and $L^{\infty}$. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to $\mathbb{R}^n$, $n \geq 3$, involving the vector-valued Riesz kernel of homogeneity $-1$ and $n-1$ of its components. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4355 10.1512/iumj.2011.60.4355 en Indiana Univ. Math. J. 60 (2011) 1319 - 1362 state-of-the-art mathematics http://iumj.org/access/