Vector valued estimates for matrix weighted maximal operators and product BMO

2024/07/23 by Kakaroumpas, Spyridon, Gibert, Odí Soler i · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2407.16776

Abstract

We consider maximal operators acting on vector valued functions, that is functions taking values on ℂ^d, that incorporate matrix weights in their definitions. We show vector valued estimates, in the sense of Fefferman--Stein inequalities, for such operators. These are proven using an extrapolation result for convex body valued functions due to Bownik and Cruz-Uribe. Finally, we show an H¹-BMO duality for matrix valued functions and we apply the previous vector valued estimates to show upper bounds for biparameter paraproducts. For the reader's convenience, we include an appendix explaining how to adapt the extrapolation for real convex body valued functions of Bownik and Cruz-Uribe to the setting of complex convex body valued functions that we treat.

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• Recent results on matrix weighted norm inequalities

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