Mirosław Baran,
Leokadia Bialas-Ciez
(2012)
The paper deals with logarithmic capacities, an important tool in pluripotential theory. We show that a class of capacities, which contains the L-capacity, has the following product property:
,
where and are respectively a compact set and a norm in (j = 1,2), and ν is a norm in , ν = ν₁⊕ₚ ν₂ with some 1 ≤ p ≤ ∞.
For a convex subset E of , denote by C(E) the standard L-capacity and by the minimal width of E, that is, the minimal Euclidean distance between two supporting hyperplanes...