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arXiv · 2506.23206

Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content

Riju Basak·You-Wei Benson Chen·Prasun Roychowdhury
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Abstract

We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $\mathcal{H}_{\infty}^β$ with $0<β\leq n$. For $0 < α< n$, we refine existing results concerning the action of the Euclidean uncentered fractional maximal function $\mathcal{M}_α$ on the functions of bounded mean oscillations (BMO) and vanishing mean oscillations (VMO). In addition, for $0 < β_1 \leq β_2 \leq n$, we establish the boundedness of the $β_2$-dimensional uncentered maximal function $\mathcal{M}^{β_2}$ on the space $\text{BMO}^{β_1}(\mathbb{R}^n)$, where $\text{BMO}^{β_1}(\mathbb{R}^n)$ denotes the mean oscillation space adapted to the dyadic Hausdorff content $\mathcal{H}_{\infty}^{β_1}$ on $\mathbb{R}^n$.

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Riju Basak, You-Wei Benson Chen, Prasun Roychowdhury. 2025-06-29. Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content. https://arxiv.org/abs/2506.23206

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