Second-order Riesz transforms associated with magnetic Schrödinger operators

The Anh Bui; Fu Ken Ly; Sibei Yang

doi:10.1016/j.jmaa.2016.01.062

Second-order Riesz transforms associated with magnetic Schrödinger operators

The Anh Bui, Fu Ken Ly^*, Sibei Yang

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

Let A=-(1i∇-a)2+V be a magnetic Schrödinger operator on Rn, where a∈Lloc2(Rn)n and 0≤V∈Lloc1(Rn). We show that Lp(Rn) boundedness of LjLkA-1 and VA-1 for some interval of p automatically implies boundedness of the same operators and their commutators on Lwp(Rn) for certain Muckenhoupt weights w, and on the Musielak-Orlicz Hardy type spaces.

Original language	English
Pages (from-to)	1196-1218
Number of pages	23
Journal	Journal of Mathematical Analysis and Applications
Volume	437
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.01.062
Publication status	Published - 15 May 2016

Keywords

Magnetic Schrödinger operator
Musielak-Orlicz Hardy space
Riesz transform
Commutator
Muckenhoupt weight

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10.1016/j.jmaa.2016.01.062

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@article{a4cbcc3ab74f4bdf94cb4000705d5f0e,

title = "Second-order Riesz transforms associated with magnetic Schr{\"o}dinger operators",

abstract = "Let A=-(1i∇-a)2+V be a magnetic Schr{\"o}dinger operator on Rn, where a∈Lloc2(Rn)n and 0≤V∈Lloc1(Rn). We show that Lp(Rn) boundedness of LjLkA-1 and VA-1 for some interval of p automatically implies boundedness of the same operators and their commutators on Lwp(Rn) for certain Muckenhoupt weights w, and on the Musielak-Orlicz Hardy type spaces.",

keywords = "Magnetic Schr{\"o}dinger operator, Musielak-Orlicz Hardy space, Riesz transform, Commutator, Muckenhoupt weight",

author = "Bui, \{The Anh\} and Ly, \{Fu Ken\} and Sibei Yang",

year = "2016",

month = may,

day = "15",

doi = "10.1016/j.jmaa.2016.01.062",

language = "English",

volume = "437",

pages = "1196--1218",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Second-order Riesz transforms associated with magnetic Schrödinger operators

AU - Bui, The Anh

AU - Ly, Fu Ken

AU - Yang, Sibei

PY - 2016/5/15

Y1 - 2016/5/15

N2 - Let A=-(1i∇-a)2+V be a magnetic Schrödinger operator on Rn, where a∈Lloc2(Rn)n and 0≤V∈Lloc1(Rn). We show that Lp(Rn) boundedness of LjLkA-1 and VA-1 for some interval of p automatically implies boundedness of the same operators and their commutators on Lwp(Rn) for certain Muckenhoupt weights w, and on the Musielak-Orlicz Hardy type spaces.

AB - Let A=-(1i∇-a)2+V be a magnetic Schrödinger operator on Rn, where a∈Lloc2(Rn)n and 0≤V∈Lloc1(Rn). We show that Lp(Rn) boundedness of LjLkA-1 and VA-1 for some interval of p automatically implies boundedness of the same operators and their commutators on Lwp(Rn) for certain Muckenhoupt weights w, and on the Musielak-Orlicz Hardy type spaces.

KW - Magnetic Schrödinger operator

KW - Musielak-Orlicz Hardy space

KW - Riesz transform

KW - Commutator

KW - Muckenhoupt weight

UR - https://www.scopus.com/pages/publications/84957437238

UR - http://purl.org/au-research/grants/arc/DP140100649

U2 - 10.1016/j.jmaa.2016.01.062

DO - 10.1016/j.jmaa.2016.01.062

M3 - Article

AN - SCOPUS:84957437238

SN - 0022-247X

VL - 437

SP - 1196

EP - 1218

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Second-order Riesz transforms associated with magnetic Schrödinger operators

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Harmonic Analysis and Partial Differential Operators

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Second-order Riesz transforms associated with magnetic Schrödinger operators

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Keywords

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Harmonic Analysis and Partial Differential Operators

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