Doubling properties of A<inf>∞</inf>

María José González; Artur Nicolau

doi:https://doi.org/10.1007/s00041-002-0030-5

Doubling properties of A<inf>∞</inf>

María José González, Artur Nicolau

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We present a new characterization of A∞ weights in terms of Carleson measures that involve the doubling properties of the weight. We prove that a doubling weight ω belongs to A∞ if and only, if |1 - ω(lz+/ω(lz-|2 dxdy/y is a Carleson measure in ℝ2+, where z = x + iy, and Iz+, Iz- denote the right and left half of the interval Iz = (x - y, x + y). A similar result holds in ℝn, n > 1.

Original language	English
Pages (from-to)	613-618
Journal	Journal of Fourier Analysis and Applications
Volume	8
DOIs	https://doi.org/10.1007/s00041-002-0030-5
Publication status	Published - 1 Jan 2002

Keywords

A weights ∞
Carleson measures
Doubling condition

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title = "Doubling properties of A∞",

abstract = "We present a new characterization of A∞ weights in terms of Carleson measures that involve the doubling properties of the weight. We prove that a doubling weight ω belongs to A∞ if and only, if |1 - ω(lz+/ω(lz-|2 dxdy/y is a Carleson measure in ℝ2+, where z = x + iy, and Iz+, Iz- denote the right and left half of the interval Iz = (x - y, x + y). A similar result holds in ℝn, n > 1.",

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AU - González, María José

AU - Nicolau, Artur

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N2 - We present a new characterization of A∞ weights in terms of Carleson measures that involve the doubling properties of the weight. We prove that a doubling weight ω belongs to A∞ if and only, if |1 - ω(lz+/ω(lz-|2 dxdy/y is a Carleson measure in ℝ2+, where z = x + iy, and Iz+, Iz- denote the right and left half of the interval Iz = (x - y, x + y). A similar result holds in ℝn, n > 1.

AB - We present a new characterization of A∞ weights in terms of Carleson measures that involve the doubling properties of the weight. We prove that a doubling weight ω belongs to A∞ if and only, if |1 - ω(lz+/ω(lz-|2 dxdy/y is a Carleson measure in ℝ2+, where z = x + iy, and Iz+, Iz- denote the right and left half of the interval Iz = (x - y, x + y). A similar result holds in ℝn, n > 1.

KW - A weights ∞

KW - Carleson measures

KW - Doubling condition

U2 - https://doi.org/10.1007/s00041-002-0030-5

DO - https://doi.org/10.1007/s00041-002-0030-5

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SN - 1069-5869

VL - 8

SP - 613

EP - 618

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

ER -

Doubling properties of A<inf>∞</inf>

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Keywords

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