Home » Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces by Donatella Danielli
Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces Donatella Danielli

Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

Donatella Danielli

Published
ISBN : 9780821839119
Paperback
119 pages
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 About the Book 

The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Carathéodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on aMoreThe object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Carathéodory 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.