English

Dyadic bi-parameter simple commutator and dyadic little BMO

Functional Analysis 2020-12-16 v2 Analysis of PDEs Classical Analysis and ODEs

Abstract

Let \bfT\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 \bfTbb\bfTbbmod \|\bfT b-b \bfT \| \asymp \|b\|_{bmo^d}. This result is well-known for many types of bi-parameter commutators, see \cite{FS}, \cite{DLWY} and \cite{DPSK} for more details.

Cite

@article{arxiv.2012.05376,
  title  = {Dyadic bi-parameter simple commutator and dyadic little BMO},
  author = {Irina Holmes and Sergei Treil and Alexander Volberg},
  journal= {arXiv preprint arXiv:2012.05376},
  year   = {2020}
}

Comments

14 pages

R2 v1 2026-06-23T20:51:34.164Z