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 $1 < p < \infty$.
From: Tailiang Liu [view email]
[v1]
Sat, 2 May 2026 16:39:20 UTC (18 KB)
[v2]
Mon, 15 Jun 2026 13:35:53 UTC (18 KB)
[v3]
Wed, 17 Jun 2026 15:49:09 UTC (17 KB)
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