BMO from dyadic BMO via expectations on product spaces of homogeneous type
Date
2013
Authors
Chen, P.
Li, J.
Ward, L.A.
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Journal of Functional Analysis, 2013; 265(10):2420-2451
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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 ApAp and dyadic ApAp, as well as one between the reverse Hölder class RHpRHp and dyadic RHpRHp, 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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Copyright 2013 Elsevier
Access Condition Notes: As per publisher website available freely after embargo period of 24 months