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arXiv · 2304.01121

Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces

Ryan Gibara·Josh Kline
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Abstract

Let $(X,d,\mu)$ be a doubling metric measure space. We consider the behaviour of the fractional maximal function $M^\alpha$ for $0\leq \alpha 0$, we additionally assume that the space is bounded. We show that $M^\alpha$ is bounded from $BMO$ to $BLO$, a subclass of $BMO$, and maps $VMO$ to itself when $\mu$ has the annular decay property. We also show by means of examples that the action of $M^\alpha$ is not continuous on these function spaces.

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Ryan Gibara, Josh Kline. 2023-04-03. Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces. https://arxiv.org/abs/2304.01121

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