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Discrete Riesz transforms and sharp metric X-p inequalities

Author(s): Naor, Assaf

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Abstract: For p epsilon [2, infinity), the metric X-p, inequality with sharp scaling parameter is proven here to hold true in L-p. The geometric consequences of this result include the following sharp statements about embeddings of L-q into Lp when 2 < q < p < infinity: the maximal 0 epsilon (0,1] for which L-q admits a bi-theta-Holder embedding into L-p equals q/p, and for m,n epsilon N, the smallest possible bi-Lipschitz distortion of any embedding into L-p of the grid 1,...,m(n) subset of l(q)(n) is bounded above and below by constant multiples (depending only on p, q) of the quantity minn((p-q)(q-2)/(q2(p-2))),m((q-2)/q).
Publication Date: Nov-2016
Electronic Publication Date: 16-Sep-2016
Citation: Naor, Assaf. (2016). Discrete Riesz transforms and sharp metric X-p inequalities. ANNALS OF MATHEMATICS, 184 (991 - 1016. doi:10.4007/annals.2016.184.3.9
DOI: doi:10.4007/annals.2016.184.3.9
ISSN: 0003-486X
EISSN: 1939-8980
Pages: 991 - 1016
Type of Material: Journal Article
Journal/Proceeding Title: ANNALS OF MATHEMATICS
Version: Author's manuscript

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