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Lectures on Analysis on Metric Spaces

  • Textbook
  • © 2001

Overview

Authors:
  1. Juha Heinonen

    1. Mathematics Department East Hall, University of Michigan, Ann Arbor, USA

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Part of the book series: Universitext (UTX)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
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  2. Covering Theorems

    • Juha Heinonen
    Pages 1-9

  3. Maximal Functions

    • Juha Heinonen
    Pages 10-13

  4. Sobolev Spaces

    • Juha Heinonen
    Pages 14-26

  5. Poincaré Inequality

    • Juha Heinonen
    Pages 27-33

  6. Sobolev Spaces on Metric Spaces

    • Juha Heinonen
    Pages 34-42

  7. Lipschitz Functions

    • Juha Heinonen
    Pages 43-48

  8. Modulus of a Curve Family, Capacity, and Upper Gradients

    • Juha Heinonen
    Pages 49-58

  9. Loewner Spaces

    • Juha Heinonen
    Pages 59-67

  10. Loewner Spaces and Poincaré Inequalities

    • Juha Heinonen
    Pages 68-77

  11. Quasisymmetric Maps: Basic Theory I

    • Juha Heinonen
    Pages 78-87

  12. Quasisymmetric Maps: Basic Theory II

    • Juha Heinonen
    Pages 88-97

  13. Quasisymmetric Embeddings of Metric Spaces in Euclidean Space

    • Juha Heinonen
    Pages 98-102

  14. Existence of Doubling Measures

    • Juha Heinonen
    Pages 103-108

  15. Doubling Measures and Quasisymmetric Maps

    • Juha Heinonen
    Pages 109-118

  16. Conformal Gauges

    • Juha Heinonen
    Pages 119-125

  17. Back Matter

    Pages 127-141
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematics Department East Hall, University of Michigan, Ann Arbor, USA

    Juha Heinonen

Bibliographic Information

  • Book Title: Lectures on Analysis on Metric Spaces

  • Authors: Juha Heinonen

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-0131-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2001

  • Hardcover ISBN: 978-0-387-95104-1Published: 21 December 2000

  • Softcover ISBN: 978-1-4612-6525-2Published: 14 September 2012

  • eBook ISBN: 978-1-4613-0131-8Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: X, 141

  • Topics: Real Functions

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