On a variant of the Hardy inequality between weighted Orlicz spaces

Agnieszka 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 -