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<p>We provide several new characterizations of <i>A</i><sub><i>p</i>,∞</sub>-matrix weights, originally introduced by A. Volberg in [<i>J. Amer. Math. Soc.</i>, <b>10</b>, 445–466 (1997)] as matrix-valued substitutes of the classical Muckenhoupt <i>A</i><sub>∞</sub> weights. In analogy with the concept of <i>A</i><sub><i>p</i></sub>-dimensions of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of <i>A</i><sub><i>p</i>,∞</sub>-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a companion article by the same authors, these results play a key role in the study of function spaces with <i>A</i><sub><i>p</i>,∞</sub>-matrix weights, which extends earlier results in the more restricted class of <i>A</i><sub><i>p</i></sub>-matrix weights.</p>

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New Characterizations and Properties of Matrix A∞ Weights

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Fan Bu,
  • Dachun Yang,
  • Wen Yuan,
  • Tuomas Hytönen

摘要

We provide several new characterizations of Ap,∞-matrix weights, originally introduced by A. Volberg in [J. Amer. Math. Soc., 10, 445–466 (1997)] as matrix-valued substitutes of the classical Muckenhoupt A∞ weights. In analogy with the concept of Ap-dimensions of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of Ap,∞-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a companion article by the same authors, these results play a key role in the study of function spaces with Ap,∞-matrix weights, which extends earlier results in the more restricted class of Ap-matrix weights.