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. A peculiarity of our approach consists of the study of the above mentioned notions in domains with an intrinsic metric.
Citation
Irina Markina. "{$p$}-module of vector measures in domains with intrinsic metric on Carnot groups." Tohoku Math. J. (2) 56 (4) 553 - 569, 2004. https://doi.org/10.2748/tmj/1113246750
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