Open Access
July, 2005 Dyadic BMO on the bidisk
Óscar Blasco, Sandra Pott
Rev. Mat. Iberoamericana 21(2): 483-510 (July, 2005).


We give several new characterizations of the dual of the dyadic Hardy space $H^{1,d}(\mathbb{T}^2)$, the so-called dyadic BMO space in two variables and denoted ${\mathrm{BMO}}^{\mathit d}_{prod}}$. These include characterizations in terms of Haar multipliers, in terms of the ``symmetrised paraproduct'' $\Lambda_b$, in terms of the rectangular BMO norms of the iterated ``sweeps'', and in terms of nested commutators with dyadic martingale transforms. We further explore the connection between ${\mathrm{BMO}}^{\mathit d}_{prod}}$ and John-Nirenberg type inequalities, and study a scale of rectangular BMO spaces.


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Óscar Blasco. Sandra Pott. "Dyadic BMO on the bidisk." Rev. Mat. Iberoamericana 21 (2) 483 - 510, July, 2005.


Published: July, 2005
First available in Project Euclid: 11 August 2005

zbMATH: 1084.42017
MathSciNet: MR2174914

Primary: 42B30 , 47B35

Keywords: BMO on the bidisk , Carleson measures , Haar multipliers

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.21 • No. 2 • July, 2005
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