rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Lectures on Analysis on Metric Spaces
  name:
    name part: Heinonen, Juha.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2001
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (x, 140 pages)
  abstract: 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: Covering theorems -- Maximal functions -- Sobolev spaces -- Poincaré, inequality -- Sobolev spaces on metric spaces -- Lipschitz functions -- Modulus of a curve family, capacity, and upper gradients -- Loewner spaces -- Loewner spaces and Poincaré, 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.
  note: by Juha Heinonen.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics
  classification: QA331.5
  classification: 515.8
  related item:
    title info:
      title: Universitext
  identifier: 9781461301318 (electronic bk.)
  identifier: 1461301319 (electronic bk.)
  identifier: 9781461265252
  identifier: 1461265258
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422203424.0
    record identifier: in00003580272
    language of cataloging:
      language term: eng