On two weight estimates for iterated commutators

Andrei K. Lerner; Sheldy Ombrosi; Israel P. Rivera-Ríos

doi:10.1016/j.jfa.2021.109153

On two weight estimates for iterated commutators

Andrei K. Lerner
, Sheldy Ombrosi
, Israel P. Rivera-Ríos

Department of Mathematics

Universidad Nacional del Sur

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

8 Scopus citations

Abstract

In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators T_b^m. Our results are new even for the first order commutator T_b¹. A new bump type necessary condition for the two-weighted boundedness of T_b^m is obtained as well. We also provide some results related to a converse to Bloom's theorem.

Original language	English
Article number	109153
Journal	Journal of Functional Analysis
Volume	281
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2021.109153
State	Published - 15 Oct 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Funding

The first author was supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927 . The second and third authors were supported by CONICET PIP 11220130100329CO and Agencia I+D+i PICT 2018-02501 . The third author was supported by Agencia I+D+i PICT 2019-00018 .

Funders	Funder number
Agencia I+D+i	PICT 2018-02501, PICT 2019-00018
Horizon 2020 Framework Programme	713927
European Commission
Consejo Nacional de Investigaciones Científicas y Técnicas	PIP 11220130100329CO
Israel Science Foundation	447/16

Keywords

Calderón-Zygmund operators
Commutators
Sparse operators
Weighted inequalities

Access to Document

10.1016/j.jfa.2021.109153

Cite this

@article{4bcfae427eb64aa0b5aabd75bf218362,

title = "On two weight estimates for iterated commutators",

abstract = "In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators Tbm. Our results are new even for the first order commutator Tb1. A new bump type necessary condition for the two-weighted boundedness of Tbm is obtained as well. We also provide some results related to a converse to Bloom's theorem.",

keywords = "Calder{\'o}n-Zygmund operators, Commutators, Sparse operators, Weighted inequalities",

author = "Lerner, \{Andrei K.\} and Sheldy Ombrosi and Rivera-R{\'i}os, \{Israel P.\}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = oct,

day = "15",

doi = "10.1016/j.jfa.2021.109153",

language = "אנגלית",

volume = "281",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "8",

}

TY - JOUR

T1 - On two weight estimates for iterated commutators

AU - Lerner, Andrei K.

AU - Ombrosi, Sheldy

AU - Rivera-Ríos, Israel P.

PY - 2021/10/15

Y1 - 2021/10/15

N2 - In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators Tbm. Our results are new even for the first order commutator Tb1. A new bump type necessary condition for the two-weighted boundedness of Tbm is obtained as well. We also provide some results related to a converse to Bloom's theorem.

AB - In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators Tbm. Our results are new even for the first order commutator Tb1. A new bump type necessary condition for the two-weighted boundedness of Tbm is obtained as well. We also provide some results related to a converse to Bloom's theorem.

KW - Calderón-Zygmund operators

KW - Commutators

KW - Sparse operators

KW - Weighted inequalities

UR - https://www.scopus.com/pages/publications/85108628844

U2 - 10.1016/j.jfa.2021.109153

DO - 10.1016/j.jfa.2021.109153

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85108628844

SN - 0022-1236

VL - 281

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

M1 - 109153

ER -

On two weight estimates for iterated commutators

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this