Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols

2017/07/04 by Joshua Isralowitz, Hyun‐Kyoung Kwon, Sandra Pott · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Approximation Theory and Sequence Spaces

paper · doi:10.1112/jlms.12053

Abstract

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.

Citations

• Vector A₂ weights and a Hardy-Littlewood maximal function
• Matrix-weighted Besov spaces
• Weighted norm inequalities for the conjugate function and Hilbert transform
• Wavelets and the Angle between Past and Future

Cited by

• On off-diagonal operators in matrix-weighted spaces
• Matrix weighted estimates on spaces of homogeneous type

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