On a variant of the Hardy inequality between weighted Orlicz spaces

• Autorzy: Agnieszka Kałamajska , Katarzyna Pietruska-Pałuba
• Języki publikacji: EN

Abstrakty

EN

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 𝓡 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 𝓡. The set 𝓡 may be smaller than the set of Hardy transforms. Bounds for constants are also given, yielding classical Hardy inequalities with best constants.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 1
• Strony: 1-28

Daty

wydano

2009

Twórcy

autor

Agnieszka Kałamajska

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Katarzyna Pietruska-Pałuba

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm193-1-1