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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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