Weighted inequalities for discrete iterated kernel operators

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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.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 develop a new method that enables us to solve the open problem of characterizing discrete inequalities for kernel operators involving suprema. More precisely, we establish necessary and sufficient conditions under which there exists a positive constant C such that (Sigma(n is an element of z)(Sigma(n)(t = -infinity) U(i, n)a(i))(q)w(n))(1/q) <= C(Sigma(n is an element of Z)a(n)(p)v(n))(1/p) holds for every sequence of nonnegative numbers where {a(n)}(nzZ) where U is a kernel satisfying certain regularity condition, 0 < p,q <= infinity and (u(n))(nzZ) and {w(n)}(nzZ) are fixed weight sequences. We do the same for the inequality (Sigma(n is an element of z)w(n)(sup-infinity<= n U(i, n) Sigma(i)(j=-infinity) a(j)](q))(1/q) <= C(Sigma(n is an element of Z)a(n)(p)v(n))(1/p) . We characterize these inequalities by conditions of both discrete and continuous nature.
dc.description.sponsorshipCzech Science Foundation [P201-18-00580S]; Shota Rustaveli National Science Foundation (SRNSF) [RVO: 67985840]; [FR17-589]
dc.description.sponsorshipThis research was supported by the grant P201-18-00580S of the Czech Science Foundation. The research of A. Gogatishvili was partially supported by RVO: 67985840 Czech Republic and by Shota Rustaveli National Science Foundation (SRNSF), grant no. FR17-589. We would like to thank the referee for his/her critical and thorough reading of the paper and for many very valuable comments and suggestions.
dc.identifier.doi10.1002/mana.202000144
dc.identifier.endpage2196
dc.identifier.issn0025-584X
dc.identifier.issn1522-2616
dc.identifier.issue11
dc.identifier.scopus2-s2.0-85141482071
dc.identifier.scopusqualityQ2
dc.identifier.startpage2171
dc.identifier.urihttps://doi.org/10.1002/mana.202000144
dc.identifier.urihttps://hdl.handle.net/20.500.12587/25873
dc.identifier.volume295
dc.identifier.wosWOS:000879284700001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWiley-V C H Verlag Gmbh
dc.relation.ispartofMathematische Nachrichten
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241229
dc.subjectkernel operator; supremum operator; weighted inequality
dc.titleWeighted inequalities for discrete iterated kernel operators
dc.typeArticle

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