Matrix-weighted bounds in variable Lebesgue spaces

2025/03/18 by Nieraeth, Zoe, Penrod, Michael · 1 citation
#42B20 #42B25 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.14398

Abstract

In this paper we prove boundedness of Calderón-Zygmund operators and the Christ-Goldberg maximal operator in the matrix-weighted variable Lebesgue spaces recently introduced by Cruz-Uribe and the second author. Our main tool to prove these bounds is through bounding a Goldberg auxiliary maximal operator. As an application, we obtain a quantitative extrapolation theorem for matrix-weighted variable Lebesgue spaces from the recent framework of directional Banach function spaces of the first author.

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• Recent results on matrix weighted norm inequalities

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