Abstract
We apply the notion of metric cotype to show that Lp admits a quasisymmetric embedding into Lq if and only if \( p\leq q \, {\rm or} \, q\leq p\leq 2\).
Mathematics Subject Classification (2000). 46B85 and 51F99.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Heinonen J. Lectures on analysis on metric spaces. Springer-Verlag, New York: Universitext; 2001.
Maurey B, Pisier G. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math.. 1976;58(1):45–90.
Mendel M, Naor A. Euclidean quotients of finite metric spaces. Adv. Math.. 2004;189(2):451–494.
M. Mendel and A. Naor. Metric cotype. Ann. of Math. (2), 168(1):247–298, 2008.
V.D. Milman and G. Schechtman. Asymptotic theory of finite-dimensional normed spaces, volume 1200 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1986. With an appendix by M. Gromov.
J. Väisälä. The free quasiworld. Freely quasiconformal and related maps in Banach spaces. In Quasiconformal geometry and dynamics (Lublin, 1996), volume 48 of Banach Center Publ., pages 55–118. Polish Acad. Sci., Warsaw, 1999.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to Jeff Cheeger for his 65th birthday
Rights and permissions
Copyright information
© 2012 Springer Basel
About this paper
Cite this paper
Naor, A. (2012). An Application of Metric Cotype to Quasisymmetric Embeddings. In: Dai, X., Rong, X. (eds) Metric and Differential Geometry. Progress in Mathematics, vol 297. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0257-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0257-4_7
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0256-7
Online ISBN: 978-3-0348-0257-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)