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arXiv · 2308.16214

Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type

Wenna Lu·Jiang Zhou
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Abstract

The purpose of this paper is to establish some characterizations of mixed central Campanato space $\mathfrak{C}^{\vec{p},\lambda}(\mathbb{R}^{n})$, via the boundedness of the commutator operators of Hardy type. Unlike the case $\lambda\geq0$, there are some technical difficulties caused by $\lambda<0$ to be overcome. In addition, an extra assumption called as the mixed version of the reverse H\"{o}lder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed $\lambda$-central Morrey space $\mathcal{B}^{\vec{p},\lambda}(\mathbb{R}^{n})$ are also derived.

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Wenna Lu, Jiang Zhou. 2023-08-30. Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type. https://arxiv.org/abs/2308.16214

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