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arXiv · 2404.16707

A self-improving property of Riesz potentials in BMO

You-Wei Benson Chen
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Abstract

In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_\alpha f \in BMO(\mathbb{R}^n) \text{ if and only if } I_\alpha f \in BMO^\beta(\mathbb{R}^n) \text{ for } \beta \in (n-\alpha,n]. \end{align*} Here $I_\alpha$ denotes the Riesz potential of order $\alpha$ and $BMO^\beta$ represents the space of functions of bounded $\beta$-dimensional mean oscillation.

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You-Wei Benson Chen. 2024-04-25. A self-improving property of Riesz potentials in BMO. https://arxiv.org/abs/2404.16707

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