We regard a system of left invariant vector fields $\mathcal{X}=\{X_1,\dots,X_k\}$ satisfying the H\"ormander condition and the related Carnot-Carath\'eodory 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.

Keywords:

Besov spaces, sub-elliptic operators, Carnot-Carathéodory metric, Hausdorff dimension Besov spaces, sub-elliptic operators, Carnot-Carathéodory metric, Hausdorff dimension

MSC Classifications:

46E35, 43A15, 28A78 show english descriptions Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
$L^p$-spaces and other function spaces on groups, semigroups, etc.
Hausdorff and packing measures 46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.
28A78 - Hausdorff and packing measures

top of page | contact us | social media | privacy | site map