Higher order Journe commutators and characterizations of multi-parameter BMO

2015/01/23 by Yumeng Ou, Stefanie Petermichl, Ou, Yumeng +3
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CA #msc:42B20

paper · pdf · doi:10.48550/arxiv.1501.05761

38 pages

openalex publication_date 2015/01/23 · arxiv created 2015/07/14 · arxiv updated 2015/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We consider iterated commutators of multiplication by a symbol function and tensor products of Hilbert or Riesz transforms. We establish mixed BMO classes of symbols that characterize boundedness of these objects in L^p. Little BMO and product BMO, big Hankel operators and iterated commutators are the base cases of our results. We use operator theoretical methods and existing profound results on iterated commutators for the Hilbert transform case, while the general result in several variables is obtained through the construction of a Journé operator that models the behavior of the multiple Hilbert transform. Upper estimates for commutators with paraproduct free Journé operators as well as weak factorisation results are proven.

Citations

• A T(b) Theorem on Product Spaces

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