Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operator

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dc.contributor.authorAyazoglu, Rabil
dc.contributor.authorEkincioglu, Ismail
dc.contributor.authorSener, S. Sule
dc.date.accessioned2024-10-04T18:48:19Z
dc.date.available2024-10-04T18:48:19Z
dc.date.issued2022
dc.departmentBayburt Üniversitesien_US
dc.description.abstractWe investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), (r = 1, 2,...), by the Hardy averaging operator A (f) (x) = 1/x integral(x)(0) f (t)dt. If the function f lies in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), it is shown that parallel to A(f) - f parallel to(p(.),alpha(.)-rp(.)) <= C parallel to f((r))parallel to(p(.),alpha(.)') where C is a positive constant. Moreover, we consider the problem of boundedness of Hardy averaging operator A in power-type weighted variable exponent grand Lebesgue spaces Lp(alpha(.))(p(.),theta) (0, 1). The sufficient criterion established on the power-type weight function alpha(.) and exponent p(.) for the Hardy averaging operator to be bounded in these spaces.en_US
dc.description.sponsorshipTUBITAK-RFBR (Russian foundation for basic research) [119N455]en_US
dc.description.sponsorshipThe authors would like to express their gratitude to the referees for his very valuable comments and suggestions. The research of I. Ekincioglu was supported by the grant of Cooperation Program 2532 TUBITAK- RFBR (Russian foundation for basic research) with agreement number no. 119N455.en_US
dc.identifier.doi10.2298/FIL2210321A
dc.identifier.endpage3330en_US
dc.identifier.issn0354-5180
dc.identifier.issue10en_US
dc.identifier.scopus2-s2.0-85143747027en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage3321en_US
dc.identifier.urihttps://doi.org/10.2298/FIL2210321A
dc.identifier.urihttp://hdl.handle.net/20.500.12403/3013
dc.identifier.volume36en_US
dc.identifier.wosWOS:000916889600011en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherUniv Nis, Fac Sci Mathen_US
dc.relation.ispartofFilomaten_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectApproximationen_US
dc.subjectHardy averaging operatoren_US
dc.subjectPower-type weighted Sobolev spaces with variable exponenten_US
dc.subjectPower-type weighted grand Lebesgue spaces with variable exponenten_US
dc.titleApproximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operatoren_US
dc.typeArticleen_US

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