BMO from dyadic BMO via expectations on product spaces of homogeneous type

Peng Chen, Ji Li*, Lesley A. Ward

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Using the random dyadic lattices developed by Hytönen and Kairema, we build up a bridge between BMO and dyadic BMO, and hence one between VMO and dyadic VMO, via expectations over dyadic lattices on spaces of homogeneous type, including both the one-parameter and product cases. We also obtain a similar relationship between Ap and dyadic Ap, as well as one between the reverse Hölder class RHp and dyadic RHp, via geometric-arithmetic expectations. These results extend the earlier theory along this line, developed by Garnett, Jones, Pipher, Ward, Xiao and Treil, to the more general setting of spaces of homogeneous type in the sense of Coifman and Weiss.

Original languageEnglish
Pages (from-to)2420-2451
Number of pages32
JournalJournal of Functional Analysis
Volume265
Issue number10
DOIs
Publication statusPublished - 15 Nov 2013
Externally publishedYes

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