Skip Navigation


Journal of the London Mathematical Society Advance Access originally published online on February 26, 2008
Journal of the London Mathematical Society 2008 77(2):524-544; doi:10.1112/jlms/jdm114
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
77/2/524    most recent
jdm114v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Pipher, J.
Right arrow Articles by Ward, L. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

BMO from dyadic BMO on the bidisc

Jill Pipher

Department of Mathematics
Brown University
Providence, RI 02912
USA

Lesley A. Ward

Department of Mathematics
Harvey Mudd College
Claremont, CA 91711
USA
ward@math.hmc.edu

We generalize to the bidisc a theorem of Garnett and Jones relating the space BMO of functions of bounded mean oscillation to its martingale counterpart, dyadic BMO. Namely, translation-averages of suitable families of dyadic BMO functions belong to BMO. As a corollary, we deduce a biparameter version of a theorem of Burgess Davis connecting the Hardy space H1 to martingale H1. We also prove the analogs of the theorem of Garnett and Jones in the one-parameter and biparameter VMO spaces of functions of vanishing mean oscillation.

The first author was supported by the NSF under grant number DMS0600389, and by a Mellon Faculty Career Enhancement Grant. The second author was supported by a Mellon Faculty Career Enhancement Grant.

2000 Mathematics Subject Classification 42B35 (primary), 42B30 (secondary).

Received May 31, 2006; revised September 3, 2007; published online February 26, 2008.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.