Lectures on analysis on metric spaces
著者
書誌事項
Lectures on analysis on metric spaces
（Universitext）
Springer, c2001
- : softcover
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注記
"A written version of lectures from a graduate course I taught at the University of Michigan in Fall 1996."--Pref., p. [vii]
Includes bibliographical references (p. [127]-135) and index
内容説明・目次
内容説明
The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.
目次
1. Covering Theorems.- 2. Maximal Functions.- 3. Sobolev Spaces.- 4. Poincare Inequality.- 5. Sobolev Spaces on Metric Spaces.- 6. Lipschitz Functions.- 7. Modulus of a Curve Family, Capacity, and Upper Gradients.- 8. Loewner Spaces.- 9. Loewner Spaces and Poincare Inequalities.- 10. Quasisymmetric Maps: Basic Theory I.- 11. Quasisymmetric Maps: Basic Theory II.- 12. Quasisymmetric Embeddings of Metric Spaces in Euclidean Space.- 13. Existence of Doubling Measures.- 14. Doubling Measures and Quasisymmetric Maps.- 15. Conformal Gauges.- References.
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