Weighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator

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dc.authoridTurcinova, Hana/0000-0002-5424-9413
dc.authoridMihula, Zdenek/0000-0001-6962-7635
dc.authoridGogatishvili, Amiran/0000-0003-3459-0355
dc.authoridUnver Yildiz, Tugce/0000-0003-0414-8400
dc.authoridPick, Lubos/0000-0002-3584-1454
dc.contributor.authorGogatishvili, Amiran
dc.contributor.authorMihula, Zdenek
dc.contributor.authorPick, Lubos
dc.contributor.authorTurcinova, Hana
dc.contributor.authorUnver, Tugce
dc.date.accessioned2025-01-21T16:55:55Z
dc.date.available2025-01-21T16:55:55Z
dc.date.issued2022
dc.departmentKırıkkale Üniversitesi
dc.description.abstractWe study a three-weight inequality for the superposition of the Hardy operator and the Copson operator, namely (integral(b)(a)(integral(b)(t)integral(s)(a) f(tau)p upsilon(tau)d tau)(q/p) u(s) ds)(r/q)w(t)dt)(1/r) <= C integral(b)(a) f(t) dt, in which (a, b) is any nontrivial interval, q, r are positive real parameters and p is an element of (0, 1]. A simple change of variables can be used to obtain any weighted L-p-norm with p >= 1 on the right-hand side. Another simple change of variables can be used to equivalently turn this inequality into the one in which the Hardy and Copson operators swap their positions. We focus on characterizing those triples of weight functions (u, v, w) for which this inequality holds for all nonnegative measurable functions f with a constant independent of f. We use a newtype of approach based on an innovative method of discretization which enables us to avoid duality techniques and therefore to remove various restrictions that appear in earlier work. This paper is dedicated to Professor Stefan Samko on the occasion of his 80th birthday.
dc.description.sponsorshipCzech Science Foundation [P201-18-00580S, P201/21-01976S]; Danube Region Grant of the Czech Ministry of Education, Youth and Sports [8X2043]; Czech Academy of Sciences [RVO: 67985840]; project OPVVV CAAS [CZ.02.1.01/0.0/0.0/16_019/0000778]; Charles University [CZ.02.2.69/0.0/0.0/19_073/0016935, UNCE/SCI/023]; Primus research programme of Charles University [PRIMUS/21/SCI/002]; The Scientific and Technological Research Council of Turkey (TUBITAK) [1059B192000075]; [SVV-2020-260583]
dc.description.sponsorshipThis research was supported in part by the Grant P201-18-00580S of the Czech Science Foundation and by the Danube Region Grant No. 8X2043 of the Czech Ministry of Education, Youth and Sports. The research of A. Gogatishvili was also supported by Czech Academy of Sciences RVO: 67985840. The research of Z. Mihula was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/16_019/0000778 and by the Grant SVV-2020-260583. The research of L. Pick was supported in part by the Grant P201/21-01976S of the Czech Science Foundation. The research of H. Tur.cinova was supported in part by the Grant Schemes at Charles University, Reg. No. CZ.02.2.69/0.0/0.0/19_073/0016935, by the Primus research programme PRIMUS/21/SCI/002 of Charles University, by the Grant SVV-2020-260583 and Charles University Research Program No. UNCE/SCI/023. The research of T. Unver was supported by the Grant of The Scientific and Technological Research Council of Turkey (TUBITAK), Grant No.: 1059B192000075. Part of the work on this project was carried out during the meeting Per Partes held at Horni Lyse.ciny, June 2-6, 2021.
dc.identifier.doi10.1007/s00041-022-09918-6
dc.identifier.issn1069-5869
dc.identifier.issn1531-5851
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85126218539
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s00041-022-09918-6
dc.identifier.urihttps://hdl.handle.net/20.500.12587/25872
dc.identifier.volume28
dc.identifier.wosWOS:000768834700001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Birkhauser
dc.relation.ispartofJournal of Fourier Analysis and Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241229
dc.subjectWeighted Hardy inequality; Superposition of operators; Copson operator; Hardy operator; 26D10
dc.titleWeighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator
dc.typeArticle

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