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arXiv · 2110.13657

Riesz capacities of a set due to Dobiński

Nicola Arcozzi·Nikolaos Chalmoukis
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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.

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Nicola Arcozzi, Nikolaos Chalmoukis. 2021-11-11. Riesz capacities of a set due to Dobiński. https://doi.org/10.5802/crmath.332

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