Abstract

AbstractWe regard a system of left invariant vector fields satisfying the Hörmander condition and the related Carnot-Carathéodory metric on a unimodular Lie group G. We define Besov spaces corresponding to the sub-Laplacian both with positive and negative smoothness. The atomic decomposition of the spaces is given. In consequence we get the distributional characterization of the Hausdorff dimension of Borel subsets with the Haar measure zero.

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