6533b834fe1ef96bd129cd86
RESEARCH PRODUCT
Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities
Toni Heikkinensubject
Discrete mathematicsArticle Subjectlcsh:MathematicsFunction (mathematics)Space (mathematics)lcsh:QA1-939Measure (mathematics)Sobolev spacesymbols.namesakePoincaré conjectureMetric (mathematics)symbolsAnalysisMathematicsdescription
Let Φ be anN-function. We show that a functionu∈LΦ(ℝn)belongs to the Orlicz-Sobolev spaceW1,Φ(ℝn)if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 | Journal of Function Spaces and Applications |