Conformally Invariant Besov Spaces on Chord-Arc Domains

Liu Tailiang; Shen Yuliang; Yang Yaosong

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arXiv · 2605.01526

Conformally Invariant Besov Spaces on Chord-Arc Domains

Liu Tailiang·Shen Yuliang·Yang Yaosong

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Abstract

Let $\Gamma$ be a rectifiable Jordan curve. We introduce the associated Besov $p$-spaces on $\Gamma$ and in its complementary domains, and characterize chord-arc curves by the natural trace isomorphisms among these spaces. We prove the characterization for the previously unresolved range $1<p<2$, thereby extending the known results $p\geq2$ to $1<p<\infty$. We further give an alternative proof for $p\geq2$.

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Liu Tailiang, Shen Yuliang, Yang Yaosong. 2026-05-02. Conformally Invariant Besov Spaces on Chord-Arc Domains. https://arxiv.org/abs/2605.01526

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