Talk:Hardy's inequality
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mistakes in introduction
[edit]The statements in the introduction "If the right-hand side is finite, equality holds if and only if a n = 0 {\displaystyle a_{n}=0} a_{n}=0 for all n." is wrong.
The RHS is also finite if a_{n} = 0 for all n larger than some fixed n. Such a sequence is admissible. In fact, the proof in Section "Discrete version: Direct proof" has this result as an intermediate step.
- No, for instance if a_1 = 1 and all others vanish, the LHS is zeta(p), which is certainly not equal to (p/(p-1))^p. Numerically, for a_1, a_2 non-zero and all others vanishing the inequality remains strict. I don't know the general proof though. — Preceding unsigned comment added by 89.159.50.176 (talk) 12:19, 30 November 2023 (UTC)