Weighted inequalities involving Hardy and Copson operators

Basit Öğe Kaydı
dc.authoridGogatishvili, Amiran/0000-0003-3459-0355
dc.authoridPick, Lubos/0000-0002-3584-1454
dc.contributor.authorGogatishvili, Amiran
dc.contributor.authorPick, Lubos
dc.contributor.authorUnver, Tugce
dc.date.accessioned2025-01-21T16:55:56Z
dc.date.available2025-01-21T16:55:56Z
dc.date.issued2022
dc.departmentKırıkkale Üniversitesi
dc.description.abstractWe characterize a four-weight inequality involving the Hardy operator and the Copson operator. More precisely, given p(1), p(2), q(1), q(2) is an element of (0, infinity), we find necessary and sufficient conditions on non-negative measurable functions u(1), u(2), v(1), v(2) on (0, infinity) for which there exists a positive constant c such that the inequality (integral(infinity)(0)(integral(t)(0)f(s)(p2) v(2)(s)(p2)ds)(q2/p2) u(2)(t)(q2)dt)(1/q2) <= c(integral(infinity)(0)(integral(infinity)(t)f(s)(p1) v(1) (s)(p1) ds)(q1/p1) u(1)(t)(q1)dt)(1/q1) holds for every non-negative measurable function f on (0, infinity). 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 Cop(p1,q1)(u(1), v(1)) and weighted Cesaro spaces Ces(p2,q2)(u(2), v(2)), and also between spaces S-q(w) equipped with the norm parallel to f parallel to(Sq(w)) = (integral(infinity)(0)[f**(t) - f*(t)](q)w(t) dt)(1/q) and classical Lorentz spaces of type Lambda. (C) 2022 Published by Elsevier Inc.
dc.identifier.doi10.1016/j.jfa.2022.109719
dc.identifier.issn0022-1236
dc.identifier.issn1096-0783
dc.identifier.issue12
dc.identifier.scopus2-s2.0-85138994981
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.jfa.2022.109719
dc.identifier.urihttps://hdl.handle.net/20.500.12587/25874
dc.identifier.volume283
dc.identifier.wosWOS:000870529700006
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAcademic Press Inc Elsevier Science
dc.relation.ispartofJournal of Functional Analysis
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241229
dc.subjectHardy operator; Copson operator; Weighted inequality; Discretization
dc.titleWeighted inequalities involving Hardy and Copson operators
dc.typeArticle

Dosyalar

Koleksiyon

WOS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu