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There are several characterizations of coarse embeddability of locally finite metric spaces into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces L p (μ), we get their coarse embeddability into a Hilbert space for 0 < p < 2. This together with a theorem by Banach and Mazur yields that coarse embeddability into l 2 and into Lp(0,1) are equivalent when 1 ≤ p < 2. A theorem by G.Yu and the above allow us to extend to L p (μ), 0 < p < 2, the range of spaces, coarse embeddings into which is guaranteed for a finitely generated group Γ to satisfy the Novikov Conjecture.

Coarse embeddings of metric spaces into Banach spaces