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)

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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 · c) buidhe 23:05, 25 October 2020 (UTC)

• Support per nom.--Ortizesp (talk) 13:02, 26 October 2020 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.