Comptes Rendus. Mathématique (Jun 2022)
Riesz capacities of a set due to Dobiński
Abstract
We study the Riesz $(a,p)$-capacity of the so called Dobiński set. We characterize the values of the parameters $a$ and $p$ for which the $(a,p)$-Riesz capacity of the Dobiński set is positive. In particular we show that the Dobiński set has positive logarithmic capacity, thus answering a question of Dayan, Fernandéz and González. We approach the problem by considering the dyadic analogues of the Riesz $(a,p)$-capacities which seem to be better adapted to the problem.
Keywords