We study the Riesz -capacity of the so called Dobiński set. We characterize the values of the parameters and for which the -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 -capacities which seem to be better adapted to the problem.

Riesz capacities of a set due to Dobiński.

Arcozzi, Nicola;Chalmoukis, Nikolaos
2022

Abstract

We study the Riesz -capacity of the so called Dobiński set. We characterize the values of the parameters and for which the -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 -capacities which seem to be better adapted to the problem.
2022
Arcozzi, Nicola; Chalmoukis, Nikolaos
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/903721
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