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Lectures on Analysis on Metric Spaces : Universitext - Juha Heinonen

Lectures on Analysis on Metric Spaces

Universitext

Hardcover Published: 21st December 2000
ISBN: 9780387951041
Number Of Pages: 141

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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.

Covering theorems
Maximal functions
Sobolev spaces
Poincare, inequality
Sobolev spaces on metric spaces
Lipschitz functions
Modulus of a curve family, capacity, and upper gradients
Loewner spaces
Loewner spaces and Poincare, inequalities
Quasisymmetric maps. Basic theory I
Quasisymmetric maps. Basic theory II
Quasisymmetric embeddings of metric spaces in Euclidean space
Existence of doubling measures
Doubling measures and quasisymmetric maps
Conformal gauges
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387951041
ISBN-10: 0387951040
Series: Universitext
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 141
Published: 21st December 2000
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.44 x 16.28  x 1.32
Weight (kg): 0.35

Earn 162 Qantas Points
on this Book