A general approach to weighted L p rellich type inequalities related to greiner operator

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dc.contributor.authorKömbe, İsmail
dc.contributor.authorYener, Abdullah
dc.date.accessioned2020-11-21T15:54:07Z
dc.date.available2020-11-21T15:54:07Z
dc.date.issued2019en_US
dc.departmentİstanbul Ticaret Üniversitesien_US
dc.description.abstractIn this paper we exhibit some sufficient conditions that imply general weighted L p Rellich type inequality related to Greiner operator without assuming a priori symmetric hypotheses on the weights. More precisely, we prove that given two nonnegative functions a and b, if there exists a positive supersolution ? of the Greiner operator ? ? such that ? ? (a|? ? ?| p-2 ? ? ?)?b? p-1 almost everywhere in R 2n+1 ; then a and b satisfy a weighted L p Rellich type inequality. Here, p > 1 and ? ? = ? n j=1 (x 2 j +y 2 j ) is the sub-elliptic operator generated by the Greiner vector fields x j {equation presented} where (z,l)=(x,y,l)? R 2n+1 =R n ×R n ×R,|Z|={equation presented} and k ? 1. The method we use is quite practical and constructive to obtain both known and new weighted Rellich type inequalities. On the other hand, we also establish a sharp weighted L p Rellich type inequality that connects first to second order derivatives and several improved versions of two-weight L p Rellich type inequalities associated to the Greiner operator ? ? on smooth bounded domains ? in R 2n+1 . © 2019 American Institute of Mathematical Sciences. All Rights Reserved.en_US
dc.identifier.doi10.3934/cpaa.2019042en_US
dc.identifier.endpage886en_US
dc.identifier.issn1534-0392
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85054952423en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage869en_US
dc.identifier.urihttps://doi.org/10.3934/cpaa.2019042
dc.identifier.urihttps://hdl.handle.net/11467/3765
dc.identifier.volume18en_US
dc.identifier.wosWOS:000446873800015en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.ispartofCommunications on Pure and Applied Analysisen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectGreiner operatoren_US
dc.subjectRemainder termen_US
dc.subjectWeighted Rellich inequalityen_US
dc.titleA general approach to weighted L p rellich type inequalities related to greiner operatoren_US
dc.typeArticleen_US

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