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BMO from dyadic BMO on the bidisc
Author(s) -
Pipher Jill,
Ward Lesley A.
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm114
Subject(s) - bounded mean oscillation , mathematics , corollary , martingale (probability theory) , pure mathematics , hardy space , bounded function , space (punctuation) , mathematical analysis , statistics , linguistics , philosophy
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 H 1 to martingale H 1 . 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.