We study the Riesz (a,p)-capacity of the so called Dobinski set. We characterize the values of the parameters a and p for which the (a,p)-Riesz capacity of the Dobínski set is positive. In particular we show that the Dobínski set has positive logarithmic capacity, thus answering a question of Dayan, Fernandez and Gonzalez.We approach the problem by considering the dyadic analogues of the Riesz (a,p)-capacities which seem to be better adapted to the problem.
Arcozzi, N., Chalmoukis, N. (2022). Riesz capacities of a set due to Dobinski. COMPTES RENDUS MATHÉMATIQUE, 360(1), 679-685 [10.5802/crmath.332].
Riesz capacities of a set due to Dobinski
Chalmoukis, N
2022
Abstract
We study the Riesz (a,p)-capacity of the so called Dobinski set. We characterize the values of the parameters a and p for which the (a,p)-Riesz capacity of the Dobínski set is positive. In particular we show that the Dobínski set has positive logarithmic capacity, thus answering a question of Dayan, Fernandez and Gonzalez.We approach the problem by considering the dyadic analogues of the Riesz (a,p)-capacities which seem to be better adapted to the problem.
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