Talk:Hölder's inequality

From Wikipedia, the free encyclopedia

What about the generalized inequality of Hölder?

I have removed the following nonsense

[edit] Generalizations

Hölder's inequality can be generalized to lessen requirements on its two parameters. While p ≥ 1 and q ≥ 1, with 1/p + 1/q = 1, one has in terms of any two positive numbers, r > 0 and s > 0:

provided only that the integrability conditions can be generalized as well, namely that f is in L^r(S) and g is in L^s(S).

The latter inequality can be derived from Hölder's inequality applied to where . (Igny 19:59, 7 April 2006 (UTC))

---

I can understand that this generalization can be considered irrelevant, but I don't see why it is nonsense

In particular, because you can not lessen requirements on the parameters by introducing different parameters.(Igny 20:33, 7 November 2006 (UTC))

Ok. You mean it is not a generalization, but a consequence or corollary. Right?

Yes, an unimportant corollary. (Igny 16:55, 30 November 2006 (UTC))

Thanks for the clarification. My interest in this was only that I corrected the wrong 'proof' that was originally given for that fact on this page, so I wanted to know if I had made a mistake. At the time I did not feel comfortable totally removing something that was put by someone else. However I totally agree with you on the decision. (GBlanchard 10:44, 4 December 2006 (UTC))