BMO from dyadic BMO on the bidisc

被引：22

作者：

Pipher, Jill ^{[1
]}

Ward, Lesley A. ^{[2
]}

机构：

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

[2] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2008年 / 77卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1112/jlms/jdm114

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：524 / 544

页数：21

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