Dalenc, Laurent; Ou, Yumeng Upper bound for multi-parameter iterated commutators. (English) Zbl 1333.42018 Publ. Mat., Barc. 60, No. 1, 191-220 (2016). Summary: We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón-Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen’s representation theorem of Calderón-Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates. Cited in 18 Documents MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35 Function spaces arising in harmonic analysis Keywords:iterated commutators; Calderón-Zygmund operators; product BMO space; multi-parameter paraproducts; dyadic shifts PDF BibTeX XML Cite \textit{L. Dalenc} and \textit{Y. Ou}, Publ. Mat., Barc. 60, No. 1, 191--220 (2016; Zbl 1333.42018) Full Text: DOI arXiv OpenURL