We define the extremal length of horizontal vector measures on a Carnot group and study capacities associated with linear
sub-elliptic equations. The coincidence between the definition of the $p$-module of horizontal vector measure system and two different definitions of the $p$-capacity is proved. We show the continuity property of a $p$-module generated by a family of horizontal vector measures. Reciprocal relations between the $p$-capacity and $q$-module $(1/p+1/q=1)$ of horizontal vector measures are obtained. A peculiarity of our approach consists of the study of the above mentioned notions in domains with an intrinsic metric.
@article{1113246750,
author = {Markina, Irina},
title = {{$p$}-module of vector measures in domains with intrinsic metric on Carnot groups},
journal = {Tohoku Math. J. (2)},
volume = {56},
number = {1},
year = {2004},
pages = { 553-569},
language = {en},
url = {http://dml.mathdoc.fr/item/1113246750}
}
Markina, Irina. {$p$}-module of vector measures in domains with intrinsic metric on Carnot groups. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp. 553-569. http://gdmltest.u-ga.fr/item/1113246750/