Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
著者
書誌事項
Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
（Memoirs of the American Mathematical Society, no. 857）
American Mathematical Society, c2006
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注記
"Volume 182, number 857 (first of 4 numbers)"
Bibliography: p. 111-119
内容説明・目次
内容説明
The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Caratheodory 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.
目次
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.
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