A $(ϕ_n, ϕ)$-Poincaré inequality on John domain
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909205047279616 |
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| author | Feng, Shangying Liang, Tian |
| author_facet | Feng, Shangying Liang, Tian |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $(ϕ_n, ϕ)$-Poincaré inequality on John domain Feng, Shangying Liang, Tian Functional Analysis 42B35 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. |
| title | A $(ϕ_n, ϕ)$-Poincaré inequality on John domain |
| topic | Functional Analysis 42B35 |
| url | https://arxiv.org/abs/2403.17943 |