In this paper, let Formula: see text and Formula: see text be the potential along the moment curve Formula: see text (Formula: see text) defined by setting, for any suitable function Formula: see text, Formula: see text The authors obtain some equivalent characterizations via capacities of the embedding Formula: see text from Lebesgue spaces Formula: see text associated with the Formula: see text-dimensional Lebesgue measure to Formula: see text endowed with the non-negative Radon measure Formula: see text in the form of Formula: see text for a weight Formula: see text. The main ingredient of this article lies in the different approach to the estimate of the capacity of the anisotropic cubes Formula: see text along Formula: see text.
Fu et al. (Fri,) studied this question.