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Universitext

Lectures on Analysis on Metric Spaces

Authors: Heinonen, Juha

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About this Textbook

Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. 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 relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar. The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.

Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-1-4613-0131-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.99
price for USA in USD
  • ISBN 978-0-387-95104-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA in USD
  • ISBN 978-1-4612-6525-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Analysis on Metric Spaces
Authors
Series Title
Universitext
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4613-0131-8
DOI
10.1007/978-1-4613-0131-8
Hardcover ISBN
978-0-387-95104-1
Softcover ISBN
978-1-4612-6525-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 141
Topics

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