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Hardy's inequality and ultrametric matrices

✍ Scribed by John Todd; Richard S. Varga

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 114 KB
Volume: 302-303
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10168-4

No coin nor oath required. For personal study only.

✦ Synopsis

For any p > 1 and for any sequence f j g I j1 of nonnegative numbers, a classical inequality of Hardy gives that

for each n P NY unless all j 0, where the constant pap À 1 p is best possible. Here, we investigate this inequality in the case p 2, and show how it can be interpreted in terms of symmetric ultrametric matrices. From this, a generalization of Hardy's inequality, in the case p 2, is derived.

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