Memoirs of the American Mathematical Society 2006; 119 pp; softcover Volume: 182 ISBN10: 082183911X ISBN13: 9780821839119 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/182/857
 The object of the present study is to characterize the traces of the Sobolev functions in a subRiemannian, or CarnotCarathéodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on a lower dimensional manifold, and which satisfies an Ahlfors type condition with respect to the standard Lebesgue measure. We also study the extension problem for the relevant Besov spaces. Various concrete applications to the setting of Carnot groups are analyzed in detail and an application to the solvability of the subelliptic Neumann problem is presented. Table of Contents  Introduction
 Carnot groups
 The characteristic set
 \(X\)variation, \(X\)perimeter and surface measure
 Geometric estimates from above on CC balls for the perimeter measure
 Geometric estimates from below on CC balls for the perimeter measure
 Fine differentiability properties of Sobolev functions
 Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure
 The extension theorem for a Besov space with respect to a lower Ahlfors measure
 Traces on the boundary of \((\epsilon,\delta)\) domains
 The embedding of \(B^p_\beta(\Omega,d\mu)\) into \(L^q(\Omega,d\mu)\)
 Returning to Carnot groups
 The Neumann problem
 The case of Lipschitz vector fields
 Bibliography
