## Abstract

We give a quantitative embedding of the Muckenhoupt class A_{1} into A_{∞}. In particular, we show how ϵ depends on [w]A_{1} in the inequality which characterizes A∞ weights: [Formula presented] where Q is any dyadic cube and E is any subset of Q. This embedding yields a sharp reverse-Hölder inequality as an easy corollary.

Original language | English (US) |
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Pages (from-to) | 4455-4470 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2016 American Mathematical Society.

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