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Nörlund Operators On lp

Published online by Cambridge University Press:  20 November 2018

David Borwein
David Borwein*
Affiliation:
Department of Mathematics University of Western Ontario London, Ontario N6A 5B7
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Abstract

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The Nörlund matrix Na is the triangular matrix {an-k /An}, where an ≥ 0 and An := a0 + a1 + • • • + an > 0. It is proved that, subject to the existence of α := lim nan/An, Na ∊ B(lp) for 1 < p < ∞ if and only if α < ∞. It is also proved that it is possible to have Na ∊ B(lp) for 1 < p < ∞ when sup nan/An = ∞.

Keywords

47B3747A3040G05Nörlundoperators on lpnorm estimates.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 8 - 14
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Borwein, D. and Cass, F. P., Nörlund matrices as bounded operators on lp , Archiv der Mathematik 42( 1984), 464–469.Google Scholar
2. Borwein, D. and Jakimovski, A., Matrix operators on lp , Rocky Mountain J. Math. 9(1979), 463–477.Google Scholar
3. Cass, F. P. and Kratz, W., Nörlund and weighted mean matrices as bounded operators on lp, Rocky Mountain J. Math. 20(1990), 59–74.Google Scholar
4. Hardy, G. H., An inequality for Hausdorff means, J. London Math. Soc. 18(1943), 46–50.Google Scholar