Two Distinguished Subspaces of Product BMO and the Nehari--AAK Theory for Hankel Operators on the Torus

Dyadic bi-parameter repeated commutator and dyadic product BMO

Consider a tensor product of simple dyadic shifts defined below. We prove here that for dyadic bi-parameter repeated commutator its norm can be estimated from below by Chang-Fefferman $BMO$ norm pertinent to its symbol. See Theorems in Section 8 at the end of this article. But this is done below under an extra assumption on the Haar--Fourier side of the symbol. In Section 7 we carefully analyze what goes wrong in the absence of this extra assumption. At the end of this note we also list a counterexample to the existing proof of characterization of bi-parameter repeated commutator with the Hilb…

从Schatten-Hankel算子恢复乘积BMO

Recovering Product BMO from Schatten Hankel operators

研究证明小Hankel算子属于Schatten类时，其符号属于乘积BMO，扩展了Nehari定理的条件。

Vectorial Hankel operators, Carleson embeddings, and notions of $BMOA$

We consider operators of the type $D^α:H^2(\mathcal{H})\to H^2(\mathcal{H})$, where $D^α$ denotes a fractional differentiation operator, and $Γ_ϕ$ is a Hankel operator. For $α>0$, we characterize boundedness in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries. The first is that our main result does not extend to $α=0$, i.e. Nehari-Page BMOA is not characterized by the natural anti-analytic Carleson embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedne…