Multiplier theorems via martingale transforms

Rodrigo Bañuelos; Fabrice Baudoin; Li Chen; Yannick Sire

doi:10.1016/j.jfa.2021.109188

Multiplier theorems via martingale transforms

Rodrigo Bañuelos^*, Fabrice Baudoin, Li Chen, Yannick Sire

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

2 Citationer (Scopus)

Abstract

We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp L^p bounds for second order Riesz transforms by a limiting argument.

Originalsprog	Engelsk
Artikelnummer	109188
Tidsskrift	Journal of Functional Analysis
Vol/bind	281
Nummer	9
ISSN	0022-1236
DOI	https://doi.org/10.1016/j.jfa.2021.109188
Status	Udgivet - 1 nov. 2021
Udgivet eksternt	Ja

Adgang til dokumentet

10.1016/j.jfa.2021.109188

Andre filer og links

Link to publication in Scopus

Citationsformater

@article{415ed81632ee4e689259ca3c27e2cdc7,

title = "Multiplier theorems via martingale transforms",

abstract = "We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp Lp bounds for second order Riesz transforms by a limiting argument.",

keywords = "Martingale transforms, Multipliers, Universal bounds",

author = "Rodrigo Ba{\~n}uelos and Fabrice Baudoin and Li Chen and Yannick Sire",

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

year = "2021",

month = nov,

day = "1",

doi = "10.1016/j.jfa.2021.109188",

language = "English",

volume = "281",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "9",

}

TY - JOUR

T1 - Multiplier theorems via martingale transforms

AU - Bañuelos, Rodrigo

AU - Baudoin, Fabrice

AU - Chen, Li

AU - Sire, Yannick

PY - 2021/11/1

Y1 - 2021/11/1

N2 - We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp Lp bounds for second order Riesz transforms by a limiting argument.

AB - We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp Lp bounds for second order Riesz transforms by a limiting argument.

KW - Martingale transforms

KW - Multipliers

KW - Universal bounds

UR - http://www.scopus.com/inward/record.url?scp=85111555607&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2021.109188

DO - 10.1016/j.jfa.2021.109188

M3 - Journal article

AN - SCOPUS:85111555607

SN - 0022-1236

VL - 281

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

M1 - 109188

ER -

Multiplier theorems via martingale transforms

Abstract

Adgang til dokumentet

Andre filer og links

Fingeraftryk

Citationsformater