References & Citations
Mathematics > Functional Analysis
Title: A self-improving property of Riesz potentials in BMO
(Submitted on 25 Apr 2024)
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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