Dyadic bi-parameter simple commutator and dyadic little BMO

Let $\text{bfT}$ is a certain tensor product of simple dyadic shifts defined below. We prove here that for dyadic bi-parameter commutator the following equivalence holds $\mathrm{\parallel }\text{bfT}b-b\text{bfT}\mathrm{\parallel }\asymp \mathrm{\parallel }b{\mathrm{\parallel }}_{bm{o}^d}$. This result is well-known for many types of bi-parameter commutators, see \cite{FS}, \cite{DLWY} and \cite{DPSK} for more details.