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The Resource Lectures on analysis on metric spaces, Juha Heinonen

Lectures on analysis on metric spaces, Juha Heinonen

Label
Lectures on analysis on metric spaces
Title
Lectures on analysis on metric spaces
Statement of responsibility
Juha Heinonen
Creator
Subject
Language
eng
Summary
"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."--BOOK JACKET
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Heinonen, Juha
Dewey number
514/.32
Index
index present
LC call number
QA611.28
LC item number
.H44 2001
Literary form
non fiction
Nature of contents
bibliography
Series statement
Universitext
http://library.link/vocab/subjectName
  • Metric spaces
  • Mathematical analysis
Label
Lectures on analysis on metric spaces, Juha Heinonen
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [127]-135) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 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
  • 1.
  • 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
  • Covering Theorems
  • 15.
  • Conformal Gauges
  • 2.
  • Maximal Functions
  • 3.
  • Sobolev Spaces
  • 4.
  • Poincare Inequality
Control code
44469013
Dimensions
25 cm
Extent
x, 140 pages
Isbn
9780387951041
Isbn Type
(alk. paper)
Lccn
00056266
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Label
Lectures on analysis on metric spaces, Juha Heinonen
Publication
Bibliography note
Includes bibliographical references (pages [127]-135) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 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
  • 1.
  • 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
  • Covering Theorems
  • 15.
  • Conformal Gauges
  • 2.
  • Maximal Functions
  • 3.
  • Sobolev Spaces
  • 4.
  • Poincare Inequality
Control code
44469013
Dimensions
25 cm
Extent
x, 140 pages
Isbn
9780387951041
Isbn Type
(alk. paper)
Lccn
00056266
Media category
unmediated
Media MARC source
rdamedia
Media type code
n

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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