Irina Markina (Technical University Valparaiso)
$-module of vector measures on Carnot groups
Abstract.
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.
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