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A characterization of mixed $λ$-central $\mathrm{BMO}$ space via the commutators of Hardy type operators (2308.16108v1)

Published 30 Aug 2023 in math.FA

Abstract: In this paper, we give a characterization of mixed $\lambda$-central bounded mean oscillation space $\mathrm{CBMO}{\vec{q},\lambda}(\mathbb{R}{n})$ via the boundedness of the commutators of $n$-dimensional Hardy operator $\mathcal{H}$ and its dual operator $\mathcal{H}{*}$ on mixed Lebesgue space $L{\vec{p}}(\mathbb{R}{n})$. In addition, we also establish the boundedness of commutators $\mathcal{H}{b}$ and $\mathcal{H}{*}{b}$ generated with $\mathrm{CBMO}{\vec{q},\lambda}(\mathbb{R}{n})$ function $b$ on mixed $\lambda$-central Morrey space $\mathcal{B}{\vec{q},\lambda}(\mathbb{R}{n})$, respectively.

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