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November 2019 Noncompactness of Fourier convolution operators on Banach function spaces
Cláudio A. Fernandes, Alexei Y. Karlovich, Yuri I. Karlovich
Ann. Funct. Anal. 10(4): 553-561 (November 2019). DOI: 10.1215/20088752-2019-0013

Abstract

Let X(R) be a separable Banach function space such that the Hardy–Littlewood maximal operator M is bounded on X(R) and on its associate space X'(R). Suppose that a is a Fourier multiplier on the space X(R). We show that the Fourier convolution operator W0(a) with symbol a is compact on the space X(R) if and only if a=0. This result implies that nontrivial Fourier convolution operators on Lebesgue spaces with Muckenhoupt weights are never compact.

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Cláudio A. Fernandes. Alexei Y. Karlovich. Yuri I. Karlovich. "Noncompactness of Fourier convolution operators on Banach function spaces." Ann. Funct. Anal. 10 (4) 553 - 561, November 2019. https://doi.org/10.1215/20088752-2019-0013

Information

Received: 2 November 2018; Accepted: 10 February 2019; Published: November 2019
First available in Project Euclid: 30 October 2019

zbMATH: 07126072
MathSciNet: MR4026368
Digital Object Identifier: 10.1215/20088752-2019-0013

Subjects:
Primary: 47G10
Secondary: 46E30

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 4 • November 2019
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