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) Departamento de Analísis Matemático, Universidad de Valencia, Burjassot, 46100, Valencia, Spain
(2) Centre for Mathematical Sciences, Lund University, 22100, Lund, 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