Analyse harmonique, Combinatoire
Riesz capacities of a set due to Dobiński
Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 679-685.

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.

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DOI : 10.5802/crmath.332
Classification : 31C20, 30C85, 31A15, 11J83
Mots clés : Riesz capacity, Logarithmic capacity, Dobiński set, Dyadic capacity, Non-linear capacity, Diophantine approxmation
Arcozzi, Nicola 1 ; Chalmoukis, Nikolaos 1

1 Dipartimento di Matematica, Università di Bologna, 40126, Bologna, Italy
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Arcozzi, Nicola; Chalmoukis, Nikolaos. Riesz capacities of a set due to Dobiński. Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 679-685. doi : 10.5802/crmath.332. http://www.numdam.org/articles/10.5802/crmath.332/

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