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<p>Introduced by A. Volberg (1997), matrix <i>A</i><sub><i>p</i>,∞</sub> weights provide a suitable generalization of Muckenhoupt <i>A</i><sub>∞</sub> weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel–Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the <i>φ</i>-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calderón–Zygmund operators on these spaces. This is the first systematic study of inhomogeneous Besov–Triebel–Lizorkin-type spaces with <i>A</i><sub><i>p</i>,∞</sub>-matrix weights, but some of the results are new even when specialized to the scalar unweighted case.</p>

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Besov–Triebel–Lizorkin-type spaces with matrix A∞ weights

  • 期刊论文

  • 发表日期：

    2025年6月26日

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

摘要

Introduced by A. Volberg (1997), matrix Ap,∞ weights provide a suitable generalization of Muckenhoupt A∞ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel–Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the φ-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calderón–Zygmund operators on these spaces. This is the first systematic study of inhomogeneous Besov–Triebel–Lizorkin-type spaces with Ap,∞-matrix weights, but some of the results are new even when specialized to the scalar unweighted case.