A Schur multiplier characterization of coarse embeddability

We give a contractive Schur multiplier characterization of locally compact groups coarsely embeddable into Hilbert spaces. Consequently, all locally compact groups whose weak Haagerup constant is 1 embed coarsely into Hilbert spaces, and hence the Baum-Connes assembly map with coefficients is split-injective for such groups.
Comment: 6 pages. Final version. To appear in Bull. Bel. Math. Soc. arXiv admin note: substantial text overlap with arXiv:1408.5238