### Abstract

Let A ⊆ {1,..., N} and let {a _{n}} _{n∈Λ} be a sequence with \a _{n}\ ≤ 1 for all n. It is easy to see that || _{n∈Λ}∑a _{n}e(nθ)|| _{p}≤|| _{n∈Λ}∑e(nθ)|| _{p} for every even integer p. We give an example which shows that this statement can fail rather dramatically when p is not an even integer. This answers in the negative a question known as the Hardy-Littlewood majorant conjecture, thereby ruling out a certain approach to the restriction and Kakeya families of conjectures.

Original language | English |
---|---|

Pages (from-to) | 511-517 |

Number of pages | 7 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 137 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1 2004 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)