This is an announcement for the paper “Discrete Riesz transforms and sharp metric $X_p$ inequalities” by Assaf Naor. Abstract: For p∈[2,∞) the metric Xp inequality with sharp scaling parameter is proven here to hold true in Lp. The geometric consequences of this result include the following sharp statements about embeddings of Lq into Lp when 2<q<p<∞: the maximal θ∈(0,1] for which Lq admits a bi-θ-H\"older embedding into Lp equals q/p, and for m,n∈ℕ the smallest possible bi-Lipschitz distortion of any embedding into Lp of the grid {1,…,m}n⊆ℓnq is bounded above and below by constant multiples (depending only on p,q) of the quantity min{n(p−q)(q−2)/(q2(p−2)),m(q−2)/q}. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.03332 _______________________________________________ Banach mailing list Banach@mathdept.okstate.edu<mailto:Banach@mathdept.okstate.edu> http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach Bentuo Zheng Associate Professor, Department of Mathematical Sciences, College of Arts and Sciences [UofM logo] The University of Memphis 359 Dunn Hall Memphis, TN 38152<http://www.memphis.edu/emailsignatures/emailsignaturemac.php#> 901.678<http://www.memphis.edu/emailsignatures/emailsignaturemac.php#>.3534 | memphis.edu<http://www.memphis.edu/> [UofM tw]<https://www.facebook.com/uofmemphis> [UofM tw] <https://twitter.com/uofmemphis> [UofM tw] <https://instagram.com/uofmemphis>