Poincaré Inequalities for Mutually Singular Measures

• Autorzy: Andrea Schioppa
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Poincaré inequality; differentiable structure

Kategorie tematyczne

• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-06-10

zaakceptowano

2014-11-27

online

2015-02-02

Twórcy

autor

Andrea Schioppa

• Swiss Federal Institute of Technology in Zurich (ETHZ) Zürich

Bibliografia

• [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.
• [2] Jeff Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), no. 3, 428–517. [Crossref]
• [3] Jeff Cheeger and Bruce Kleiner, Inverse limit spaces satisfying a Poincarè inequality, Anal. Geom. Metr. Spaces 3 (2015), 15–39.
• [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]
• [5] Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1–61.
• [6] Stephen Keith, Modulus and the Poincaré inequality on metric measure spaces, Math. Z. 245 (2003), no. 2, 255–292. [WoS]
• [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]
• [8] Urs Lang and Conrad Plaut, Bilipschitz embeddings of metric spaces into space forms, Geom. Dedicata 87 (2001), no. 1-3, 285–307.
• [9] Zygmunt Zahorski, Sur l’ensemble des points de non-dérivabilité d’une fonction continue, Bull. Soc. Math. France 74 (1946), 147–178.

Identyfikatory

DOI

10.1515/agms-2015-0003