BMO from dyadic BMO via expectations on product spaces of homogeneous type |
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Authors: | Peng Chen Ji Li Lesley A. Ward |
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Affiliation: | 1. School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA 5095, Australia;2. Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, PR China |
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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. |
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Keywords: | Spaces of homogeneous type Multiparameter harmonic analysis Random dyadic lattices BMO VMO Hardy spaces Ap weights Reverse Hö lder weights Dyadic function classes |
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