On a variant of the Hardy inequality between weighted Orlicz spaces
Agnieszka Kałamajska ; Katarzyna Pietruska-Pałuba
Studia Mathematica, Tome 192 (2009), p. 1-28 / Harvested from The Polish Digital Mathematics Library
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Let M be an N-function satisfying the Δ₂-condition, and let ω, φ be two other functions, with ω ≥ 0. We study Hardy-type inequalities ∫ℝ₊M(ω(x)|u(x)|)exp(-φ(x))dx≤C∫ℝ₊M(|u'(x)|)exp(-φ(x))dx, where u belongs to some set of locally absolutely continuous functions containing C₀∞(ℝ₊). We give sufficient conditions on the triple (ω,φ,M) for such inequalities to be valid for all u from a given set . The set may be smaller than the set of Hardy transforms. Bounds for constants are also given, yielding classical Hardy inequalities with best constants.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:285211 
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Agnieszka Kałamajska; Katarzyna Pietruska-Pałuba. On a variant of the Hardy inequality between weighted Orlicz spaces. Studia Mathematica, Tome 192 (2009) pp. 1-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-1/