Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space

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A map f between two metric spaces (X,d₁) and (Y,d₂) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi₁, phi₂:[0,∞) --> [0,∞) such that: phi₁(d₁(x,y)) ≤ d₂(f(x),f(y)) ≤ phi₂(d₁(x,y)) for all x, y in X, and phi₁(t) tends to ∞ as t tends to ∞. We characterize those quasi-Banach spaces that have a coarse embedding into a Hilbert space.