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Lower Bounds for Matrices, II

Published online by Cambridge University Press:  20 November 2018

Grahame Bennett
Grahame Bennett*
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A.
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Abstract

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Our main result is the following monotonicity property for moment sequences μ. Let p be fixed, 1 ≤ p < ∞: then

is an increasing function of r(r = 1,2,…). From this we derive a sharp lower bound for an arbitrary Hausdorff matrix acting on ℓp.The corresponding upper bound problem was solved by Hardy.

Keywords

26D1540G0547A3047B37
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 54 - 74
Copyright
Copyright © Canadian Mathematical Society 1991

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