Conformally Invariant Besov Spaces on Chord-Arc Domains

Summary · qwen2.5:32b

The article introduces Besov-type spaces on simply connected domains, proving that on quasidisks, first-order Besov spaces are isomorphic to higher-order counterparts, which preserve conformal quasi-invariance. This characterization of chord-arc domains through the isomorphism between first-order and boundary Besov spaces extends previous Dirichlet space ($p=2$) results to all $1 < p < \infty$.

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Mathematical analysis of conformally invariant Besov spaces on simply connected domains and their application to chord-arc domains.

Excerpt

arXiv:2605.01526v4 Announce Type: replace Abstract: Inspired by the classical Besov $p$-spaces defined via higher-order derivatives on the upper half-plane, we introduce Besov-type spaces on simply connected domains. We first prove that on quasidisks, the first-order Besov space is isomorphic to its higher-order counterparts, and that these higher-order spaces preserve conformal quasi-invariance. Based on this result, we characterize chord-arc domains in terms of the isomorphism between the first-order Besov space and the boundary Besov space. This extends recent results for the Dirichlet space ($p=2$) to the general case $1 < p < \infty$.