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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

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4. Hardy, G. H., An inequality for Hausdorff means, J. London Math. Soc. 18(1943), 46–50.Google Scholar