Abstract

We introduce the \(p\)-adic weighted central Campanato spaces \(\dot{C}^{q,\lambda}(\omega)(\mathbb{Q}_{p}^{n})\) and characterize \(\dot{C}^{q,\lambda}(\omega)(\mathbb{Q}_{p}^{n})\) by the boundedness of the commutators of \(p\)-adic \(n\)-dimensional Hardy operators on \(p\)-adic weighted central Morrey spaces for \(\omega\in A_{1}(\mathbb{Q}_{p}^{n})\). In particular, the characterizations of \(p\)-adic weighted central \(BMO\) spaces are also obtained.

中文翻译：

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通过$$p$$-Adic Hardy Operators Commutator 表征 $$p$$ -Adic 加权中央 Campanato 空间

摘要

我们引入\(p\) -adic 加权中心 Campanato 空间\(\dot{C}^{q,\lambda}(\omega)(\mathbb{Q}_{p}^{n})\)和用\(\dot{C}^{q,\lambda}(\omega)(\mathbb{Q}_{p}^{n})\)通过\(p\) -adic的交换子的有界性来表征\(n\)维 Hardy 算子在\(p\) -adic 加权中心 Morrey 空间上用于\(\omega\in A_{1}(\mathbb{Q}_{p}^{n})\)。特别地，还获得了\(p\) -adic 加权中心\(BMO\)空间的特征。