Thinness of sets in potential theory associated with local Muckenhoupt weights
Volume 136 / 2026
Annales Polonici Mathematici 136 (2026), 75-100
MSC: Primary 31C15; Secondary 31C40
DOI: 10.4064/ap241214-10-7
Published online: 21 January 2026
Abstract
We study the thinness of sets with respect to weighted local Riesz capacities, where the associated weights are of local Muckenhoupt class. The thinness is characterized in terms of Wolff potentials. We also obtain the Kellogg property and Choquet theorem as applications.
