Revista Matemática Iberoamericana

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Volume 21, Issue 2, 2005, pp. 483–510
DOI: 10.4171/RMI/427

Dyadic BMO on the bidisk

Óscar Blasco[1] and Sandra Pott[2]

(1) Universidad de Valencia, Spain
(2) Lund University, Sweden

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.

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

Blasco Óscar, Pott Sandra: Dyadic BMO on the bidisk. Rev. Mat. Iberoamericana 21 (2005), 483-510. doi: 10.4171/RMI/427