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arXiv · 2310.10135

Choquet integrals, Hausdorff content and sparse operators

Naoya Hatano·Ryota Kawasumi·Hiroki Saito·Hitoshi Tanaka
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Abstract

Let $H^d$, $0 0$. In this paper we verify that the sparse operator ${\mathcal A}_{{\mathcal S}}$ maps ${\mathcal L}^p(H^d)$, $1\le p<\infty$, into an associate space of Orlicz-Morrey space ${{\mathcal M}^{p'}_{\Phi_0}(H^d)}'$, $\Phi_0(t)=t\log(e+t)$. We also give another characterizations of those associate spaces using the tiling ${\mathcal T}$ of ${\mathbb R}^n$.

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Naoya Hatano, Ryota Kawasumi, Hiroki Saito, Hitoshi Tanaka. 2023-10-16. Choquet integrals, Hausdorff content and sparse operators. https://arxiv.org/abs/2310.10135

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