混合赫兹空间的外推法及其应用

Pub Date : 2024-03-03 DOI:10.1002/mana.202100134

Mingquan Wei

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引用次数: 0

摘要

在本文中，我们将外推法理论扩展到混合赫兹空间和.赫兹空间。为了证明主要结果，我们首先研究了混合赫兹空间的对偶空间，然后给出了混合赫兹空间上哈迪-利特尔伍德最大算子的有界性。通过使用外推定理，我们得到了混合赫兹空间上许多积分算子的有界性。我们还给出了通过混合赫兹空间上一些算子换元的有界性的新特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Extrapolation to mixed Herz spaces and its applications

In this paper, we extend the extrapolation theory to mixed Herz spaces ${\dot{K}}_{\vec{q}}^{α, p} (R^{n})$ and $K_{\vec{q}}^{α, p} (R^{n})$ . To prove the main result, we first study the dual spaces of mixed Herz spaces, and then give the boundedness of the Hardy–Littlewood maximal operator on mixed Herz spaces. By using the extrapolation theorems, we obtain the boundedness of many integral operators on mixed Herz spaces. We also give a new characterization of $bounded mean oscillation space (BMO) (R^{n})$ via the boundedness of commutators of some operators on mixed Herz spaces.

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