JournalsrmiVol. 21, No. 2pp. 483–510

Dyadic BMO on the bidisk

  • Óscar Blasco

    Universidad de Valencia, Spain
  • Sandra Pott

    Lund University, Sweden
Dyadic BMO on the bidisk cover
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Abstract

We give several new characterizations of the dual of the dyadic Hardy space H1,d(T2)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'' Λb\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.

Cite this article

Óscar Blasco, Sandra Pott, Dyadic BMO on the bidisk. Rev. Mat. Iberoam. 21 (2005), no. 2, pp. 483–510

DOI 10.4171/RMI/427