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arXiv · 2503.14398

Matrix-weighted bounds in variable Lebesgue spaces

Zoe Nieraeth·Michael Penrod
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Abstract

In this paper we prove boundedness of Calder\'on-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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Zoe Nieraeth, Michael Penrod. 2025-03-18. Matrix-weighted bounds in variable Lebesgue spaces. https://doi.org/10.54330/afm.164106

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