Hardy type inequality in variable Lebesgue spaces
| dc.creator | Rafeiro, Humberto | |
| dc.creator | Samko, Stefan | |
| dc.date | 2008-04-22 | |
| dc.date | 2009-02-26 | |
| dc.date.accessioned | 2026-07-07T12:46:25Z | |
| dc.date.available | 2026-07-07T12:46:25Z | |
| dc.description | We prove that in variable exponent spaces $L^{p(\cdot)}(Ω)$, where $p(\cdot)$ satisfies the log-condition and $Ω$ is a bounded domain in $\mathbf R^n$ with the property that $\mathbf R^n \backslash \barΩ$ has the cone property, the validity of the Hardy type inequality $$| 1/δ(x)^α\int_Ωϕ(y) dy/|x-y|^{n-α}|_{p(\cdot)} \leqq C |ϕ|_{p(\cdot)}, \quad 0<\al<\min(1,\frac{n}{p_+})$$, where $δ(x)=\mathrm{dist}(x,\partialΩ)$, is equivalent to a certain property of the domain $\Om$ expressed in terms of $\al$ and $χ_\Om$. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0804.3511 | |
| dc.identifier | http://arxiv.org/abs/0804.3511 | |
| dc.identifier | Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 279--289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221377 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B38; 42B35; 46E35 | |
| dc.title | Hardy type inequality in variable Lebesgue spaces | |
| dc.type | text |