On off-diagonal operators in matrix-weighted spaces

2026/07/20 by David Cruz-Uribe, Aapo Laukkarinen, Kabe Moen
#math.CA #math.FA

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Abstract

In this paper we prove matrix-weighted inequalities for fractional operators and their commutators. We do so by developing the theory of convex body domination for such operators. Using this approach we prove quantitative estimates for the fractional integral operator (or Riesz potential) and its commutators, and prove matrix-weighted Gagliardo-Nirenberg-Sobolev inequalities for vector-valued functions.

Citations

• Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols
• Matrix-weighted Besov spaces
• Vector A₂ weights and a Hardy-Littlewood maximal function
• Wavelets and the Angle between Past and Future

Related

• Some remarks on convex body domination
• Recent results on matrix weighted norm inequalities
• Matrix weighted estimates on spaces of homogeneous type
• Two weight norm inequalities for fractional integral operators and commutators
• Two Matrix Weighted Inequalities for Commutators with Fractional Integral Operators