Commutators of convolution type operators on some banach function spaces

Oleksiy Karlovych

Commutators of convolution type operators on some banach function spaces

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Abstract

We study the boundedness of Fourier convolution operators W-0 (b) and the compactness of commutators of W-0 (b) with multiplication operators al on some Banach function spaces X (14) for certain classes of piecewise quasicontinuous functions a is an element of PQC and piecewise slowly oscillating Fourier multipliers b is an element of PSO degrees(X,1). We suppose that X( I) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz Rodriguez, Yuri Karlovich, and Ivan Loreto Hernandez obtained for Lebesgue spaces with Muckenhoupt weights.

Original language	English
Pages (from-to)	191-205
Number of pages	15
Journal	Annals of functional analysis
Volume	6
Issue number	4
Publication status	Published - 2015

Keywords

Fourier convolution operator
commutator
piecewise quasicontinuous function
piecewise slowly oscillating multiplier
Banach function space
rearrangement invariant space
variable Lebesgue space
WEIGHTED NORM INEQUALITIES
LEBESGUE SPACES
ALGEBRAS

Cite this

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title = "Commutators of convolution type operators on some banach function spaces",

abstract = "We study the boundedness of Fourier convolution operators W-0 (b) and the compactness of commutators of W-0 (b) with multiplication operators al on some Banach function spaces X (14) for certain classes of piecewise quasicontinuous functions a is an element of PQC and piecewise slowly oscillating Fourier multipliers b is an element of PSO degrees(X,1). We suppose that X( I) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz Rodriguez, Yuri Karlovich, and Ivan Loreto Hernandez obtained for Lebesgue spaces with Muckenhoupt weights.",

keywords = "Fourier convolution operator, commutator, piecewise quasicontinuous function, piecewise slowly oscillating multiplier, Banach function space, rearrangement invariant space, variable Lebesgue space, WEIGHTED NORM INEQUALITIES, LEBESGUE SPACES, ALGEBRAS",

author = "Oleksiy Karlovych",

note = "Sem PDF. This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and EXPL/MAT-CAL/0840/2013 (Problemas Variacionais em Espacos de Sobolev de Expoente Variavel).",

year = "2015",

language = "English",

volume = "6",

pages = "191--205",

journal = "Annals of functional analysis",

issn = "2008-8752",

publisher = "Tusi Mathematical Research Group",

number = "4",

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T1 - Commutators of convolution type operators on some banach function spaces

AU - Karlovych, Oleksiy

N1 - Sem PDF. This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and EXPL/MAT-CAL/0840/2013 (Problemas Variacionais em Espacos de Sobolev de Expoente Variavel).

PY - 2015

Y1 - 2015

N2 - We study the boundedness of Fourier convolution operators W-0 (b) and the compactness of commutators of W-0 (b) with multiplication operators al on some Banach function spaces X (14) for certain classes of piecewise quasicontinuous functions a is an element of PQC and piecewise slowly oscillating Fourier multipliers b is an element of PSO degrees(X,1). We suppose that X( I) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz Rodriguez, Yuri Karlovich, and Ivan Loreto Hernandez obtained for Lebesgue spaces with Muckenhoupt weights.

AB - We study the boundedness of Fourier convolution operators W-0 (b) and the compactness of commutators of W-0 (b) with multiplication operators al on some Banach function spaces X (14) for certain classes of piecewise quasicontinuous functions a is an element of PQC and piecewise slowly oscillating Fourier multipliers b is an element of PSO degrees(X,1). We suppose that X( I) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz Rodriguez, Yuri Karlovich, and Ivan Loreto Hernandez obtained for Lebesgue spaces with Muckenhoupt weights.

KW - Fourier convolution operator

KW - commutator

KW - piecewise quasicontinuous function

KW - piecewise slowly oscillating multiplier

KW - Banach function space

KW - rearrangement invariant space

KW - variable Lebesgue space

KW - WEIGHTED NORM INEQUALITIES

KW - LEBESGUE SPACES

KW - ALGEBRAS

M3 - Article

SN - 2008-8752

VL - 6

SP - 191

EP - 205

JO - Annals of functional analysis

JF - Annals of functional analysis

IS - 4

ER -

Commutators of convolution type operators on some banach function spaces

Abstract

Keywords

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