\(p\)-module of vector measures in domains with intrinsic metric on Carnot groups
The author defines the extremal length of horizontal vector measures on a Carnot group and studies capacities associated with linear subelliptic equations. The coincidence between the definition of the \(p\)-module of a horizontal vector measure system and two different definitions of the \(p\)-capacity is proved. It is shown the continuity property of a \(p\)-module generated by a family of horizontal vector measures. Reciprocal relations between the \(p\)-capacity and a \(q\)-module \((1/p+1/q=1)\) of horizontal vector measures are obtained. The peculiarity of the approach consists in the study of the above mentioned notions in domains with an intrinsic metric.
scientific article; zbMATH DE number 2157244
scientific article