Cover Image

Lectures on Analysis on Metric Spaces /

Show other versions (1)

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 sett...

Full description

Bibliographic Details
Main Author: Heinonen, Juha
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York, 2001.
Series:Universitext,
Subjects:
Mathematics.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Covering theorems
  • Maximal functions
  • Sobolev spaces
  • PoincarĂ©, inequality
  • Sobolev spaces on metric spaces
  • Lipschitz functions
  • Modulus of a curve family, capacity, and upper gradients
  • Loewner spaces
  • Loewner spaces and PoincarĂ©, 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.