# On the L p -distortion of finite quotients of amenable groups

On the L p -distortion of finite quotients of amenable groups We study the L p -distortion of finite quotients of amenable groups. In particular, for every $${2\leq p < \infty}$$ , we prove that the ℓ p -distortions of the groups $${C_2\wr C_n}$$ and $${C_{2^n}\rtimes C_n}$$ are in $${\Theta((\log n)^{1/p}),}$$ and that the ℓ p -distortion of $${C_n^2 \rtimes_A \mathbf{Z}}$$ , where A is the matrix $${{\left({\small\begin{array}{cc}2 & 1 \\ 1 & 1 \end{array}} \right)}}$$ is in $${\Theta((\log \log n)^{1/p}).}$$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On the L p -distortion of finite quotients of amenable groups

, Volume 16 (4) – Jul 26, 2011
8 pages

/lp/springer_journal/on-the-l-p-distortion-of-finite-quotients-of-amenable-groups-3b9O0yqFrI
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Potential Theory; Operator Theory; Fourier Analysis; Econometrics; Calculus of Variations and Optimal Control; Optimization
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0136-6
Publisher site
See Article on Publisher Site

### Abstract

We study the L p -distortion of finite quotients of amenable groups. In particular, for every $${2\leq p < \infty}$$ , we prove that the ℓ p -distortions of the groups $${C_2\wr C_n}$$ and $${C_{2^n}\rtimes C_n}$$ are in $${\Theta((\log n)^{1/p}),}$$ and that the ℓ p -distortion of $${C_n^2 \rtimes_A \mathbf{Z}}$$ , where A is the matrix $${{\left({\small\begin{array}{cc}2 & 1 \\ 1 & 1 \end{array}} \right)}}$$ is in $${\Theta((\log \log n)^{1/p}).}$$

### Journal

PositivitySpringer Journals

Published: Jul 26, 2011

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