Optimal relationships between \((L^p)\)-norms for the Hardy operator and its dual

DOI10.1007/s10231-012-0283-9zbMath1325.47094arXiv1206.1731OpenAlexW2004999489MaRDI QIDQ2014998

Viktor I. Kolyada

Publication date: 18 June 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.1731

zbMATH Keywords

Hardy operatorsharp constantdual Hardy operator

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integral operators (47G10) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items

Hardy's operator minus identity and power weights, Weak-type and end-point norm estimates for Hardy operators, Averaging operators on decreasing or positive functions: equivalence and optimal bounds, On the optimal relationships between \(L^P\)-norms for the Hardy operator and its dual for decreasing functions, On the Cesàro and Copson norms of nonnegative sequences, Sharp inequalities between L^p-norms for the higher dimensional Hardy operator and its dual, Hardy's inequality and its descendants: a probability approach, Weighted inequalities involving Hardy and Copson operators

Cites Work

• Solution to a conjecture on the norm of the Hardy operator minus the identity
• Functional properties of rearrangement invariant spaces defined in terms of oscillations
• Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions
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