Besov capacity redux

Relations between the Besov capacities and other set functions, for example, the Hausdorff capacities are considered. A unique approach suggested here is based on the ideas of the previous works of the author, the results of Netrusov, and the classical characterization of Frostman for Hausdorff capacity. In particular, the Besov capacity C(·; B _α ^{p, q} ), α > 0, 0 < p, q ⩽ ∞, is reconsidered in light of Netrusov’s recent contribution to the subject–identifying the nature of the null sets when either p or q is less than or equal to 1. We also give a Frostman type argument to replace one of Netrusov’s arguments (for 0 < q ⩽ 1) and present a Frostman type characterization of these set functions: a condition in terms of Borel measures applied to Euclidean balls. Bibliography: 7 titles. Illustrations: 1 figure.