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arXiv · 2410.11724

Square Functions Controlling Smoothness and Higher-Order Rectifiability

John Hoffman
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Abstract

We provide new characterizations of the $BMO$-Sobolev space $I_{\alpha}(BMO)$ for the range $0 < \alpha <2$. When $0 < \alpha <1$, our characterizations are in terms of square functions measuring multiscale approximation of constants, and when $1 \leq \alpha <2$ our characterizations are in terms of square functions measuring multiscale approximation by linear functions.

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John Hoffman. 2024-10-15. Square Functions Controlling Smoothness and Higher-Order Rectifiability. https://arxiv.org/abs/2410.11724

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