Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-carathéodory spaces /

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Bibliographic Details
Author / Creator:	Danielli, Donatella, 1966-
Imprint:	Providence, R.I. : American Mathematical Society, c2006.
Description:	ix, 119 p. ; 25 cm.
Language:	English
Series:	Memoirs of the American Mathematical Society, 0065-9266 ; no. 857
Subject:	Harmonic analysis. Homogeneous spaces. Sobolev spaces. Measure theory. Differential equations, Partial. Differential equations, Partial. Harmonic analysis. Homogeneous spaces. Measure theory. Sobolev spaces.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/6004049

Hidden Bibliographic Details
Other authors / contributors:	Garofalo, Nicola. Nhieu, Duy-Minh, 1966-
ISBN:	082183911X (alk. paper)
Notes:	"Volume 182, number 857 (first of 4 numbers)." Includes bibliographical references (p. 111-119).

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

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