<abstract xmlns="http://www.w3.org/1999/xhtml">

We prove compactness of the operator <italic>MhCg</italic> on a subspace of the space of 2<italic>π</italic>-periodic functions of Riesz bounded variation on [−<italic>π, π</italic>], for appropriate functions <italic>g</italic> and <italic>h</italic>. Here <italic>Mh</italic> denotes multiplication by <italic>h</italic> and <italic>Cg</italic> convolution by <italic>g</italic>.
</abstract>

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

Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Compactness of Multiplication Operators on Riesz Bounded Variation Spaces"}

We prove compactness of the operator MhCg on a subspace of the space of 2π-periodic functions of Riesz bounded variation on [−π, π], for appropriate functions...

Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Published Online: Jan 01, 2022

Page range: 167 - 174

Received: Dec 29, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0012

Keywords
Riesz bounded variation, multiplication operator, compactness

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Published Online: Jan 01, 2022

Page range: 167 - 174

Received: Dec 29, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0012

KeywordsRiesz bounded variation, multiplication operator, compactness

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Riesz bounded variation, multiplication operator, compactness