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A many-variable Landau-Kolmogorov inequality

Published online by Cambridge University Press:  24 October 2008

Khristo N. Boyadzhiev
Khristo N. Boyadzhiev
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences
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Extract

The Landau–Kolmogorov inequality

where ‖.‖ is the ‘sup’ norm, is well known and has many interesting applications and generalizations (see [1, 4–7, 13, 16]). Its study was initiated by Landau[10] and Hadamard [8] (the case n = 2). Kolmogorov [9] succeeded in finding in explicit form the best possible constants K(n, k) = Cn, k in (1) for functions on the whole real line R. The best constants for the half line R+ are not known in explicit form except for n = 2, 3, 4, but an algorithm exists for their computation (Schoenberg and Cavaretta [15]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 123 - 129
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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