This article studies strong -weights and Besov capacities as well as their relationship to Hausdorff measures. It is shown that in the Euclidean space with , whenever , a function yields a strong -weight of the form if the distributional gradient has sufficiently small -norm. Similarly, it is proved that if , then is a strong -weight whenever the Besov -seminorm of is sufficiently small. Lower estimates of the Besov -capacities are obtained in terms of the Hausdorff content associated with gauge functions satisfying the condition .
Cite this article
Șerban Costea, Strong -weights and scaling invariant Besov capacities. Rev. Mat. Iberoam. 23 (2007), no. 3, pp. 1067–1114DOI 10.4171/RMI/524