Iterated Hardy-type inequalities involving suprema

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dc.contributor.authorGogatishvili, Amiran
dc.contributor.authorMustafayev, Rza Ch.
dc.date.accessioned2020-06-25T18:22:41Z
dc.date.available2020-06-25T18:22:41Z
dc.date.issued2017
dc.departmentKırıkkale Üniversitesi
dc.descriptionGogatishvili, Amiran/0000-0003-3459-0355; Gogatishvili, Amiran/0000-0003-3459-0355; Mustafayev, Rza/0000-0002-2806-9646
dc.description.abstractIn this paper, the boundedness of the composition of the supremal operators defined, for a non-negative measurable functions f on (0,infinity), by S(u)g(t) := ess sup(0<tau <= t) u(tau)g(tau), t is an element of(0,infinity), and S*(u)g(t) := ess sup(t <=tau<infinity) u(tau)g(tau), t is an element of(0,infinity), where u is a fixed continous weight on (0,infinity), with the Hardy and Copson operators between weighted Lebesgue spaces L-p(v) and L-q(w) are characterized. The complete solution of the restricted inequalities, that is, inequalities parallel to S-u(f)parallel to(q,w(0,infinity)) <= c parallel to f parallel to(p,v,(0,infinity)), and parallel to S-u(f)parallel to(q,w(0,infinity)) <= c parallel to f parallel to(p,v,(0,infinity)), being satisfied on the cones of monotone functions f on (0,infinity), are given. Moreover, the complete characterization of the inequality parallel to T(u,b)f parallel to(q,w,(0,infinity)) <= c parallel to f parallel to(p,v,(0,infinity)), being satisfied for every non-negative and non-increasing functions f on (0,infinity), is given for 0 < p, q < infinity, as well. Here the operator T-u,T-b is defined for a measurable non-negative function f on (0,infinity) by (T(u,b)g)(t) := sup(t <=tau<infinity) u(tau)/B(tau) integral(tau)(0) g(s)b(s) ds, t is an element of (0,infinity), where u, b are two weight functions on (0,infinity) such that u is continuous on (0,infinity) and the function B(t) := integral(t)(0)b(s) ds satisfies 0 < B(t) < infinity for every t is an element of (0,infinity).en_US
dc.description.sponsorshipGrant Agency of the Czech RepublicGrant Agency of the Czech Republic [P201-13-14743S]; Shota Rustaveli National Science Foundation [31/48, DI/9/5-100/13]; Academy of Sciences of Czech RepublicCzech Academy of Sciences; Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK); RVO [67985840]en_US
dc.description.sponsorshipThe research of A. Gogatishvili was partly supported by the grants P201-13-14743S of the Grant Agency of the Czech Republic and RVO: 67985840, by Shota Rustaveli National Science Foundation grants no. 31/48 (Operators in some function spaces and their applications in Fourier Analysis) and no. DI/9/5-100/13 (Function spaces, weighted inequalities for integral operators and problems of summability of Fourier series). The research of both authors was partly supported by the joint project between Academy of Sciences of Czech Republic and The Scientific and Technological Research Council of Turkey.en_US
dc.identifier.citationGogatishvili, Amiran & Mustafayev, Rza. (2015). Iterated Hardy-type inequalities involving suprema. Mathematical Inequalities and Applications. 20. 10.7153/mia-2017-20-57.en_US
dc.identifier.doi10.7153/mia-2017-20-57
dc.identifier.endpage927en_US
dc.identifier.issn1331-4343
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85031692681
dc.identifier.scopusqualityQ1
dc.identifier.startpage901en_US
dc.identifier.urihttps://doi.org/10.7153/mia-2017-20-57
dc.identifier.urihttps://hdl.handle.net/20.500.12587/6863
dc.identifier.volume20en_US
dc.identifier.wosWOS:000412831800001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElementen_US
dc.relation.ispartofMathematical Inequalities & Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectQuasilinear operatorsen_US
dc.subjectiterated Hardy inequalitiesen_US
dc.subjectweightsen_US
dc.titleIterated Hardy-type inequalities involving supremaen_US
dc.typeArticle

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