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Weighted Convolution Operators on ℓp

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Werner Kratz
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7 e-mail: [email protected]
Werner Kratz
Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, 89073 Ulm, Germany e-mail: [email protected]
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Abstract

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The main results deal with conditions for the validity of the weighted convolution inequality ${{\sum }_{n\in \mathbb{Z}}}|{{b}_{n}}\,{{\sum }_{k\in \mathbb{Z}}}{{a}_{n-{{k}^{x}}k}}{{|}^{p}}\,\le \,{{C}^{p\,}}\,{{\sum }_{k\in \mathbb{Z}}}\,{{\left| {{x}_{k}} \right|}^{p}}$ when $p\,\ge \,1$.

Keywords

40G1040E05convolution operators on ℓp
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 175 - 179
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Borwein, D. and Cass, F. P., Nörlund matrices as bounded operators on lp . Arch. Math. 42(1984), 464–469.Google Scholar
[2] Borwein, D.. Nörlund operators on lp . Canad. Math. Bull. 36(1993), 8–14.Google Scholar
[3] Wilansky, A., Functional Analysis. Blaisdell, New York, 1964.Google Scholar