Palepson

Welcome to the Wikipedia, and about your edits to the "Bounded Mean Oscillation" entry

Hello and welcome to the Wikipedia: I am Daniele Tampieri and I sometimes contribute to the Bounded mean oscillation entry. I have moved your contribution to a special section in the entry, since their emphasis is mainly on the one dimensional theory: I also restored the section on the Fefferman's theorem since it is the multi-dimensional theorem which is dealt in the sources given. Let me know if this is not acceptable for you: also, I would like to collaborate with you to this entry, if you like: I know quite well the basic multi-dimensional theory of functions of bounded mean oscillation, but I am not a specialist in the theory of BMOH/BMOA. Can you add some references on the subject to the entry? Daniele.tampieri (talk) 13:45, 4 April 2011 (UTC)

Sorry I hastily deleted it :( (didn't think about it). My name is Christos chatzifountas . The case i wrote is not the one dimensional it merely uses one dimensional BMO on the sircle to define the BMOH of the disc (thus the change from I to D in H(D)). The point is that currently the research is centered on analytic and harmonic hardy spaces, and when you use the term "Hardy space" mean the analytic Hardy space in the disc or in the plane (one can use the one or the other and with some care the results are interchangeable) so i changed the one that used Fefermans notation to the more current "real valued harmonic Hardy spaces".The rest of the notation about BMO is used "as is". Also i plan to put something about the VMOA, the dual of H^1(D) (or $H^{1}(R_{+}^{2})$). Thank you for correcting the entries and if you find something ambiguous please do it again :)

I added at the end Daniel' notes they are pretty advanced and cover pretty much everything in the subject. Of course there are other applications of bmo (in probability theory and PDES) if you want ot take a look there are references there

Thank you very much for your work and for your answer: as you may have guessed, I am not a specialist in the theory of functions of bounded mean oscillation (it is a topic I'll focus on maybe next year), and I use the book of Stein (and John's original works) as the main reference for my edits. I cured the historical section since BMO was used in the theory of elasticity from the very first time, and I am interested in continuum mechanics. As you see, I reproduced the statement about the BMO/H¹ without any discussion, therefore if you thought it was too hazy, you did the right thing removing it: maybe in the next future we'll plan the structure of the entry and give it a more precise and correct formal statement (also in the future I'll plan to add an application section including application to PDE and other (possibly continuum mechanics) :D), therefore feel free to make all the additions you think right: Finally, let me to give you a few advices I found of some value during my edits in Wikipedia:

• Remember to add as many references as possible: this helps you in defend your edits from arbitrary deletions, movings and so on, and also helps the reader who wants to approach the subject.
• Give to the entry a as general as possible scope: even topics that aren't currently mainstream are of interest, since it aims to be an encyclopedia entry, not (only) an advanced survey.
• Also remember to sign your comments by using the four tildes ~~~~.

At last, I must say that there was another editor who contributed to the entry: his name is Jazzam. Well, I hope I haven't bored you too much :D Daniele.tampieri (talk) 13:26, 12 April 2011 (UTC)

P.S. Maybe you'll find interesting this show-up of citation templates: there are many, but I advice you to use the {{Citation}}. It is way more powerful and versatile than the others. :D Daniele.tampieri (talk) 15:59, 12 April 2011 (UTC)

Thank you in return. I see you also corrected the notation and added "half-space" which is indeed the right one :D . I currently work on spaces of analytic functions - Hardy and Bergam space. BMO(A) has many interesting properties like comformaly invariance of the norm, many equivalent norm definitions, is a subspace of all H^p coincidence with the Bloch space (the dual of A^1 the analytic L^1 function) in 1-1 functions and so on. If you want any help with BMO-VMO or a reference, do not hesitate to contact me

I imagined that it was a typo since you stated the correct concept just before: I am not a specialist in BMO, but I am quite interested in boundary values (in various senses) of various classes of functions (harmonic, holomorphic and so on). I already asked for a copy of the paper by Girela (it has a very positive review in Zbl) to the Math. Dept. of Joensuu University. My main research is focused on partial differential equations, but now I am studying the Python programming language in order to improve my professional skills. If you need some advices on editing on Wikipedia, you know how to find me. :D Daniele.tampieri (talk) 12:41, 13 April 2011 (UTC)