Talk:Orlicz space

Query
Who calls these Birnbaum-Orlicz spaces? No offense to Prof. Birnbaum, but I've always heard them referred to as Orlicz spaces. Shall we start calling L^p a Banach-Wiener spaces? — Preceding unsigned comment added by 139.67.20.36 (talk) 15:22, 21 April 2016 (UTC)


 * The term Birnbaum-Orlicz is sometimes used in the literature; see this paper for example. However, these spaces are typically referred to as Orlicz spaces. I believe this is something we should highlight in the article. Sopasakis p (talk) 11:25, 28 December 2017 (UTC)

Is that stuff really in Evans's book or is the reference vacuous? I quickly checked my copy and found nothing on Orlicz or Orlicz-Sobolev spaces. Matti Nuortio, Oulu, Finland 14:27, 18 April 2007 (UTC)


 * See the Sobolev emebdding theorems for the "boundary case" k p = n. Sullivan.t.j 14:34, 18 April 2007 (UTC)

Orlicz-Sobolev spaces?
Are there Orlicz space-based Sobolev spaces? Temur (talk) 07:18, 28 December 2007 (UTC)


 * Yes, and they are called Orlicz-Sobolev spaces, exactly as you guessed. A Google Scholar search on those words will turn up a lot of papers. Perturbationist (talk) 01:59, 30 December 2007 (UTC)

L1 and Orlicz axioms
The L1 space for p=1 does not seem to satisfy the axioms of an Orlicz norm, since \Psi(t) = t is the only reasonable choice, yet t^-1*\Psi(t) does not have the claimed limit properties. Yet the article claims Birnbaum-Orlicz spaces generalize Lebesgue spaces.

--2001:638:906:2:5054:FF:FE4D:41C4 (talk) 12:41, 12 October 2012 (UTC)


 * Well, it generalizes Lebesgue spaces, except for L1 and L∞. Boris Tsirelson (talk) 12:54, 27 March 2015 (UTC)


 * Actually $$\Psi(t) = |t|$$ is a Young function. I find it strange that, according to this article, a Young function must satisfy $$\lim_{t\to 0}\Psi(t)/t = 0$$. This is not the case according to the book of M. Ledoux and M. Talagrand, neither according to any other references I have read. I believe we need to rectify this post. Sopasakis p (talk) 11:25, 28 December 2017 (UTC)


 * I also have a question about $$\lim_{t\to 0}\Psi(t)/t = 0$$. I have been working on this, and I always see people require $$\Psi(0)=0$$. The 0 limit condition seems to be too strong.

Requested move 17 October 2020

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: Consensus to move (non-admin closure) BegbertBiggs (talk) 10:56, 2 November 2020 (UTC)

Birnbaum–Orlicz space → Orlicz space – As explained in the article, the shorter name is by far more common and, according to professionals, more justified historically. Tarnoob (talk) 22:50, 17 October 2020 (UTC) —Relisting. (t &#183; c)  buidhe  23:05, 25 October 2020 (UTC)
 * Support per nom.--Ortizesp (talk) 13:02, 26 October 2020 (UTC)