Two nonequivalent conditions for weight functions

Charles Fefferman; Benjamin Muckenhoupt

doi:10.1090/S0002-9939-1974-0360952-X

Two nonequivalent conditions for weight functions

Charles Fefferman, Benjamin Muckenhoupt

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

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)
Pages (from-to)	99-104
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	45
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1974-0360952-X
State	Published - Jul 1974
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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Cite this

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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∞.",

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AU - Muckenhoupt, Benjamin

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AB - 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∞.

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Two nonequivalent conditions for weight functions

Abstract

All Science Journal Classification (ASJC) codes

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