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arXiv · 2311.05974

New Characterizations and Properties of Matrix $A_\infty$ Weights

Fan Bu·Tuomas Hytönen·Dachun Yang·Wen Yuan
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Abstract

We provide several new characterizations of $A_{p,\infty}$-matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_\infty$ weights. In analogy with the notion of $A_p$-dimension of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of $A_{p,\infty}$-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a follow-up work, these results will play a key role in the study of function spaces with $A_{p,\infty}$-matrix weights, which extends earlier results in the more restricted class of $A_p$-matrix weights.

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Fan Bu, Tuomas Hytönen, Dachun Yang, Wen Yuan. 2023-11-10. New Characterizations and Properties of Matrix $A_\infty$ Weights. https://arxiv.org/abs/2311.05974

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