p (p>2) does not coarsely embed into a Hilbert space
W. B. Johnson, N. L. Randrianarivony
Abstract
A coarse embedding of a metric space X into a metric space Y is a map f: X-->Y satisfying for every x, y in X: ϕ1(d(x,y)) ≤ d(f(x),f(y)) ≤ ϕ2(d(x,y)) where ϕ1 and ϕ2 are nondecreasing functions on [0,∞) with values in [0,∞), with the condition that ϕ1(t) tends to ∞ as t tends to ∞. We show that p does not coarsely embed in a Hilbert space for 2<p<∞.
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