Poincaré Inequalities for Mutually Singular Measures
Andrea Schioppa
Analysis and Geometry in Metric Spaces, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:268821 
@article{bwmeta1.element.doi-10_1515_agms-2015-0003,
     author = {Andrea Schioppa},
     title = {Poincar\'e Inequalities for Mutually Singular Measures},
     journal = {Analysis and Geometry in Metric Spaces},
     volume = {3},
     year = {2015},
     zbl = {1310.26017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0003}
}

Andrea Schioppa. Poincaré Inequalities for Mutually Singular Measures. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0003/

[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. | Zbl 1088.28002

[2] Jeff Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), no. 3, 428–517. [Crossref] | Zbl 0942.58018

[3] Jeff Cheeger and Bruce Kleiner, Inverse limit spaces satisfying a Poincarè inequality, Anal. Geom. Metr. Spaces 3 (2015), 15–39. | Zbl 1331.46016

[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] | Zbl 1277.46012

[5] Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1–61. | Zbl 0915.30018

[6] Stephen Keith, Modulus and the Poincaré inequality on metric measure spaces, Math. Z. 245 (2003), no. 2, 255–292. [WoS] | Zbl 1037.31009

[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] | Zbl 0962.30006

[8] Urs Lang and Conrad Plaut, Bilipschitz embeddings of metric spaces into space forms, Geom. Dedicata 87 (2001), no. 1-3, 285–307. | Zbl 1024.54013

[9] Zygmunt Zahorski, Sur l’ensemble des points de non-dérivabilité d’une fonction continue, Bull. Soc. Math. France 74 (1946), 147–178. | Zbl 0061.11302