### Abstract

A nonnegative function on the real line satisfies the condition A∞ if, given ∊ > 0, there exists a δ > 0 such that if I is an interval, E ⊂ I, and |E| < δ|I|, then. A nonnegative function on the real line satisfies the condition A if for every interval I, where 2I is the interval with the same center as I and twice as long, and C is independent of I. An example is given of a function that satisfies A but not A∞.

Original language | English (US) |
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Pages (from-to) | 99-104 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 45 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1974 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Fefferman, C., & Muckenhoupt, B. (1974). Two nonequivalent conditions for weight functions.

*Proceedings of the American Mathematical Society*,*45*(1), 99-104. https://doi.org/10.1090/S0002-9939-1974-0360952-X