# On a variant of the Hardy inequality between weighted Orlicz spaces

Agnieszka Kałamajska; Katarzyna Pietruska-Pałuba

Studia Mathematica (2009)

- Volume: 193, Issue: 1, page 1-28
- ISSN: 0039-3223

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topAgnieszka Kałamajska, and Katarzyna Pietruska-Pałuba. "On a variant of the Hardy inequality between weighted Orlicz spaces." Studia Mathematica 193.1 (2009): 1-28. <http://eudml.org/doc/285211>.

@article{AgnieszkaKałamajska2009,

abstract = {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
$∫_\{ℝ₊\} M(ω(x)|u(x)|) exp(-φ(x)) dx ≤ C ∫_\{ℝ₊\} M(|u^\{\prime \}(x)|) exp(-φ(x)) dx$,
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.},

author = {Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba},

journal = {Studia Mathematica},

keywords = {Hardy inequalities; weighted Orlicz spaces},

language = {eng},

number = {1},

pages = {1-28},

title = {On a variant of the Hardy inequality between weighted Orlicz spaces},

url = {http://eudml.org/doc/285211},

volume = {193},

year = {2009},

}

TY - JOUR

AU - Agnieszka Kałamajska

AU - Katarzyna Pietruska-Pałuba

TI - On a variant of the Hardy inequality between weighted Orlicz spaces

JO - Studia Mathematica

PY - 2009

VL - 193

IS - 1

SP - 1

EP - 28

AB - 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
$∫_{ℝ₊} M(ω(x)|u(x)|) exp(-φ(x)) dx ≤ C ∫_{ℝ₊} M(|u^{\prime }(x)|) exp(-φ(x)) dx$,
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.

LA - eng

KW - Hardy inequalities; weighted Orlicz spaces

UR - http://eudml.org/doc/285211

ER -

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