The measures with an associated square function operator bounded in L2

Benjamin Jaye; Fedor Nazarov; Xavier Tolsa

doi:10.1016/j.aim.2018.09.025

The measures with an associated square function operator bounded in L²

Benjamin Jaye, Fedor Nazarov, Xavier Tolsa

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Abstract

© 2018 Elsevier Inc. In this paper we provide an extension of a theorem of David and Semmes [3] to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in L2. The description is given in terms of a modification of Jones’ β-coefficients.

Original language	English
Pages (from-to)	60-112
Journal	Advances in Mathematics
Volume	339
DOIs	https://doi.org/10.1016/j.aim.2018.09.025
Publication status	Published - 1 Dec 2018

Keywords

Geometric measure theory
Singular integral operators

Access to Document

10.1016/j.aim.2018.09.025

Cite this

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abstract = "{\textcopyright} 2018 Elsevier Inc. In this paper we provide an extension of a theorem of David and Semmes [3] to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in L2. The description is given in terms of a modification of Jones{\textquoteright} β-coefficients.",

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AU - Nazarov, Fedor

AU - Tolsa, Xavier

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N2 - © 2018 Elsevier Inc. In this paper we provide an extension of a theorem of David and Semmes [3] to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in L2. The description is given in terms of a modification of Jones’ β-coefficients.

AB - © 2018 Elsevier Inc. In this paper we provide an extension of a theorem of David and Semmes [3] to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in L2. The description is given in terms of a modification of Jones’ β-coefficients.

KW - Geometric measure theory

KW - Singular integral operators

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DO - 10.1016/j.aim.2018.09.025

M3 - Article

VL - 339

SP - 60

EP - 112

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708