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Concrete Operators

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Banach algebra of the Fourier multipliers on weighted Banach function spaces

Alexei Karlovich
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  • Centro de Matemática e Aplicações, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516 Caparica, Portugal
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Published Online: 2015-03-10 | DOI: https://doi.org/10.1515/conop-2015-0001


Let MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L(ℝ) is that MX,w(ℝ) is a Banach algebra.

Keywords : Fourier convolution operator; Fourier multiplier; Banach function space; Cauchy singular integral operator; rearrangement-invariant space; variable Lebesgue space; Muckenhoupt-type weight


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About the article

Received: 2015-01-28

Accepted: 2015-02-23

Published Online: 2015-03-10

Citation Information: Concrete Operators, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2015-0001.

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© 2015 Alexei Karlovich. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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