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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17943 |
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Table of Contents:
- Given a bounded domain $Ω\subset {\mathbb R}^{n}$ with $n\ge2$, let $ϕ$ is a Young function satisfying the doubling condition with the constant $K_ϕ<2^{n}$. If $Ω$ is a John domain, we show that $Ω$ supports a $(ϕ_{n}, ϕ)$-Poincaré inequality. Conversely, assume additionally that $Ω$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\ge3$. If $Ω$ supports a $(ϕ_n, ϕ)$-Poincaré inequality, we show that it is a John domain.