Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Martha Guzmán-Partida

doi:10.2478/tmmp-2021-0012

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Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Tatra Mountains Mathematical Publications

Volume 78 (2021): Issue 1 (October 2021)

By: Martha Guzmán-Partida

Open Access

|Jan 2022

Abstract

We prove compactness of the operator M_hC_g on a subspace of the space of 2π-periodic functions of Riesz bounded variation on [−π, π], for appropriate functions g and h. Here M_h denotes multiplication by h and C_g convolution by g.

References

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[2] HANCHE-OLSEN, H.—HOLDEN, H.: The Kolmogorov-Riesz compactness theorem, Expo. Math. 28 (2010), no. 4, 385–394.
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[3] JORDAN, C.: Sur la série de Fourier, C. R. Math. Acad. Sci. Paris 2 (1881), 228–230.
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[4] RIESZ, F.: Untersuchungen über Systeme integrierbarer Funktionen, Math. Ann. 69 (1910), no. 4, 449–497.
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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0012 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 167 - 174

Submitted on: Dec 29, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Riesz bounded variation,

multiplication operator,

compactness

Related subjects:

Mathematics,

General mathematics

© 2022 Martha Guzmán-Partida, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 78 (2021): Issue 1 (October 2021)