Besov Spaces and Hausdorff Dimension For Some Carnot-Carathéodory Metric Spaces

Skrzypczak, Leszek

Canadian journal of mathematics, Tome 54 (2002) no. 6, pp. 1280-1304

Résumé

We regard a system of left invariant vector fields $X=\,\{{{X}_{1}},\,\ldots ,\,{{X}_{k}}\}$ 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 $\Delta \,=\,\sum X_{i}^{2}$ 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.

Détail

DOI : 10.4153/CJM-2002-049-x

Mots-clés : 46E35, 43A15, 28A78, Besov spaces, sub-elliptic operators, Carnot-Carathéodory metric, Hausdorff dimension

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