Commutators for fourier multipliers on Besov spaces

Joan Cerdà; Joaquim Martín

doi:https://doi.org/10.1016/j.jat.2004.03.007

Commutators for fourier multipliers on Besov spaces

Joan Cerdà, Joaquim Martín

Department of Mathematics

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

2 Citations (Scopus)

Abstract

If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ -TμT is bounded on Bpσ,q (Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. © 2004 Published by Elsevier Inc.

Original language	English
Pages (from-to)	119-128
Journal	Journal of Approximation Theory
Volume	129
DOIs	https://doi.org/10.1016/j.jat.2004.03.007
Publication status	Published - 1 Aug 2004

Keywords

Approximation spaces
Besov space
Commutator
Interpolation theory
K-functional
Multipliers

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title = "Commutators for fourier multipliers on Besov spaces",

abstract = "If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ -TμT is bounded on Bpσ,q (Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. {\textcopyright} 2004 Published by Elsevier Inc.",

keywords = "Approximation spaces, Besov space, Commutator, Interpolation theory, K-functional, Multipliers",

author = "Joan Cerd{\`a} and Joaquim Mart{\'i}n",

year = "2004",

month = aug,

day = "1",

doi = "https://doi.org/10.1016/j.jat.2004.03.007",

language = "English",

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T1 - Commutators for fourier multipliers on Besov spaces

AU - Cerdà, Joan

AU - Martín, Joaquim

PY - 2004/8/1

Y1 - 2004/8/1

N2 - If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ -TμT is bounded on Bpσ,q (Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. © 2004 Published by Elsevier Inc.

AB - If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ -TμT is bounded on Bpσ,q (Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. © 2004 Published by Elsevier Inc.

KW - Approximation spaces

KW - Besov space

KW - Commutator

KW - Interpolation theory

KW - K-functional

KW - Multipliers

U2 - https://doi.org/10.1016/j.jat.2004.03.007

DO - https://doi.org/10.1016/j.jat.2004.03.007

M3 - Article

VL - 129

SP - 119

EP - 128

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

ER -