Poincaré Inequalities for Mutually Singular Measures

Andrea Schioppa

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 40-45, electronic only
  • ISSN: 2299-3274

Abstract

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Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.

How to cite

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Andrea Schioppa. "Poincaré Inequalities for Mutually Singular Measures." Analysis and Geometry in Metric Spaces 3.1 (2015): 40-45, electronic only. <http://eudml.org/doc/268821>.

@article{AndreaSchioppa2015,
abstract = {Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.},
author = {Andrea Schioppa},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Poincaré inequality; differentiable structure},
language = {eng},
number = {1},
pages = {40-45, electronic only},
title = {Poincaré Inequalities for Mutually Singular Measures},
url = {http://eudml.org/doc/268821},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Andrea Schioppa
TI - Poincaré Inequalities for Mutually Singular Measures
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 40
EP - 45, electronic only
AB - Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.
LA - eng
KW - Poincaré inequality; differentiable structure
UR - http://eudml.org/doc/268821
ER -

References

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  1. [1] Giovanni Alberti,Marianna Csörnyei, and David Preiss, Structure of null sets in the plane and applications, European Congress of Mathematics, Eur. Math. Soc., Zürich, 2005, pp. 3–22.  Zbl1088.28002
  2. [2] Jeff Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), no. 3, 428–517. [Crossref] Zbl0942.58018
  3. [3] Jeff Cheeger and Bruce Kleiner, Inverse limit spaces satisfying a Poincarè inequality, Anal. Geom. Metr. Spaces 3 (2015), 15–39.  Zbl1331.46016
  4. [4] Jeff Cheeger and Bruce Kleiner, Realization of metric spaces as inverse limits, and bilipschitz embedding in L1, Geom. Funct. Anal. 23 (2013), no. 1, 96–133. [Crossref][WoS] Zbl1277.46012
  5. [5] Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1–61.  Zbl0915.30018
  6. [6] Stephen Keith, Modulus and the Poincaré inequality on metric measure spaces, Math. Z. 245 (2003), no. 2, 255–292. [WoS] Zbl1037.31009
  7. [7] T. J. Laakso, Ahlfors Q-regular spaces with arbitrary Q > 1 admitting weak Poincaré inequality, Geom. Funct. Anal. 10 (2000), no. 1, 111–123. [Crossref] Zbl0962.30006
  8. [8] Urs Lang and Conrad Plaut, Bilipschitz embeddings of metric spaces into space forms, Geom. Dedicata 87 (2001), no. 1-3, 285–307.  Zbl1024.54013
  9. [9] Zygmunt Zahorski, Sur l’ensemble des points de non-dérivabilité d’une fonction continue, Bull. Soc. Math. France 74 (1946), 147–178.  Zbl0061.11302

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