On a variant of Hardy inequality between weighted Orlicz spaces
| dc.creator | Kalamajska, Agnieszka | |
| dc.creator | Pietruska-Paluba, Katarzyna | |
| dc.date | 2009-03-26 | |
| dc.date.accessioned | 2026-07-07T12:57:06Z | |
| dc.date.available | 2026-07-07T12:57:06Z | |
| dc.description | Let M be an N-function satisfying the $Δ_2$- condition, let $ω, \vp$ be two other functions, $ω\ge 0$. We study Hardy-type inequalities \[ \int_{\rp} M(ω(x)|u(x)|) {\rm exp}(-\vp (x))dx \le C\int_{\rp} M(|u'(x)|) {\rm exp}(-\vp (x))dx, \] where $u$ belongs to some dilation invariant set ${\cal R}$ contained in the space of locally absolutely continuous functions. We give sufficient conditions the triple $(ω,\vp,M)$ must satisfy in order to have such inequalities valid for $u$ from a given set ${\cal R}$. The set ${\cal R}$ can be smaller than the set of Hardy transforms. Bounds for constants, retrieving classical Hardy inequalities with best constants, are also given. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0903.4624 | |
| dc.identifier | http://arxiv.org/abs/0903.4624 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224814 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 26D10, 46E35 | |
| dc.title | On a variant of Hardy inequality between weighted Orlicz spaces | |
| dc.type | text |