2020/01/30 by Joshua Isralowitz, Sandra Pott, Isralowitz, Joshua +3 · 2 citations
Computer Science · Mathematics · #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2001.11182
openalex publication_date 2020/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of research initiated by the first two authors.