Weighted inequalities involving Hardy and Copson operators

0562000 - MÚ 2023 RIV US eng J - Journal Article
Gogatishvili, Amiran - Pick, L. - Tuğçe, Ünver
Weighted inequalities involving Hardy and Copson operators.
Journal of Functional Analysis. Roč. 283, č. 12 (2022), č. článku 109719. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA ČR(CZ) GA18-00580S
Institutional support: RVO:67985840
Keywords : Hardy operator * Copson operator * weighted inequality * discretization
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jfa.2022.109719

We characterize a four-weight inequality involving the Hardy operator and the Copson operator. The proof is based on discretizing and antidiscretizing techniques. The principal innovation consists in development of a new method which carefully avoids duality techniques and therefore enables us to obtain the characterization in previously unavailable situations, solving thereby a long-standing open problem. We then apply the characterization of the inequality to the establishing of criteria for embeddings between weighted Copson spaces and weighted Cesàro spaces.
Permanent Link: https://hdl.handle.net/11104/0334425