Annals of Functional Analysis

Commutators of convolution type operators on some Banach function spaces

Alexei Yu Karlovich

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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 $aI$ on some Banach function spaces $X(\mathbb{R})$ for certain classes of piecewise quasicontinuous functions $a\in PQC$ and piecewise slowly oscillating Fourier multipliers $b\in PSO_{X,1}^\diamond$. We suppose that $X(\mathbb{R})$ 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--Rodríguez, Yuri Karlovich, and Iván Loreto Hernández obtained for Lebesgue spaces with Muckenhoupt weights.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 4 (2015), 191-205.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764011

Digital Object Identifier
doi:10.15352/afa/06-4-191

Mathematical Reviews number (MathSciNet)
MR3365991

Zentralblatt MATH identifier
1335.47021

Subjects
Primary: 47B47: Commutators, derivations, elementary operators, etc.
Secondary: 42A45: Multipliers 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Fourier convolution operator commutator piecewise quasicontinuous function piecewise slowly oscillating multiplier Banach function space rearrangement-invariant space variable Lebesgue space

Citation

Karlovich, Alexei Yu. Commutators of convolution type operators on some Banach function spaces. Ann. Funct. Anal. 6 (2015), no. 4, 191--205. doi:10.15352/afa/06-4-191. https://projecteuclid.org/euclid.afa/1435764011


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