2015/07/31 by Joshua Isralowitz, Hyun‐Kyoung Kwon, Hyun-Kyoung Kwon +1 · 23 citations
Mathematics · #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Commutator #Embedding #Holomorphic and Operator Theory #Mathematical proof #Matrix (chemical analysis) #Matrix function #Matrix norm #Norm (philosophy) #Pascal matrix #math.CA #msc:42B20
paper · pdf · doi:10.1112/jlms.12053
published in Journal of the London Mathematical Society 96(1), 243-270 (Wiley) · v2, 38 pages, minor changes made (including a shorter proof of (b) implies (a) in Theorem 1.3), to appear in the Journal of the London Mathematical Society
openalex created_date 2016/06/24 · arxiv created 2017/03/17 · openalex publication_date 2017/07/04 · arxiv updated 2017/07/12 · openalex updated_date 2026/08/05
Abstract Let be a locally integrable matrix function, a matrix A weight with , and be any of the Riesz transforms. We will characterize the boundedness of the commutator on in terms of the membership of in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to prove sharp bounds for the Christ/Goldberg matrix weighted maximal function associated with matrix A weights.