Whitney-type theorems on extension of functions on Carnot groups

The classical Whitney's Theorem about extension of functions of various smoothness classes was generalized to Carnot groups. A Carnot group is defined as a connected simply connected Lie group whose Lie Algebra is graded. Various properties of differential operators were analyzed with respect to the Taylor polynomial on the Carnot group. The Lipschitz spaces for a particular variable (γ) were analyzed for different values of γ and more general moduli of continuity.