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

Research output: Contribution to journal › Article › Research

2 Citations (Scopus)

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

Fingerprint Dive into the research topics of 'The measures with an associated square function operator bounded in L<sup>2</sup>'. Together they form a unique fingerprint.

Cite this

@article{38ae96d88bbf48aaa321f3690cf42db6,

title = "The measures with an associated square function operator bounded in L2",

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.",

keywords = "Geometric measure theory, Singular integral operators",

author = "Benjamin Jaye and Fedor Nazarov and Xavier Tolsa",

year = "2018",

month = dec,

day = "1",

doi = "10.1016/j.aim.2018.09.025",

language = "English",

volume = "339",

pages = "60--112",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - The measures with an associated square function operator bounded in L2

AU - Jaye, Benjamin

AU - Nazarov, Fedor

AU - Tolsa, Xavier

PY - 2018/12/1

Y1 - 2018/12/1

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

U2 - 10.1016/j.aim.2018.09.025

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

ER -