On the boundedness of a B-Riesz potential in the generalized weighted B-Morrey spaces

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dc.authorid56263218000
dc.authorid24341144100
dc.contributor.authorAyazoglu R.
dc.contributor.authorHasanov J.J.
dc.date.accessioned20.04.201910:49:12
dc.date.accessioned2019-04-20T21:43:36Z
dc.date.available20.04.201910:49:12
dc.date.available2019-04-20T21:43:36Z
dc.date.issued2016
dc.departmentBayburt Üniversitesien_US
dc.description.abstractWe consider the generalized shift operator associated with the Laplace-Bessel differential operator ? B = i=1 n 2 x i 2 +i=1 k ? i x ix i .$ \Delta -{B}=\sum -{i=1}^{n}\frac{\partial ^2 }{\partial x-i^2} +\sum -{i=1}^{k} \frac{\gamma -i }{x-i}\frac{\partial }{\partial x-i}. $ The maximal operator M ? ${M-{\gamma }}$ (B-maximal operator) and the Riesz potential I ?,? ${I-{\alpha ,\gamma }}$ (B-Riesz potential), associated with the generalized shift operator are investigated. We prove that the B-maximal operator M ? ${M-{\gamma }}$ and the B-singular integral operator are bounded from the generalized weighted B-Morrey space p,? 1 ,?,? (k,+ n )${{\cal M}-{p,\omega -1,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ to p,? 2 ,?,? (k,+ n )${{\cal M}-{p,\omega -2,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ for all 1<p<${1 &lt; p &lt; \infty }$ , ?A p,? (k,+ n )${\varphi \in A-{p,\gamma }(\mathbb {R}-{k,+}^{n})}$ . Furthermore, we prove that the B-Riesz potential I ?,? ${I-{\alpha ,\gamma }}$ , 0<?<n+|?|${0&lt;\alpha &lt;n+|\gamma |}$ , is bounded from the generalized weighted B-Morrey space p,? 1 ,?,? (k,+ n )${{\cal M}-{p,\omega -1,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ to q,? 2 ,?,? (k,+ n )${{\cal M}-{q,\omega -2,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ , where ?/(n+|?|)=1/p-1/q${{\alpha }/{(n+|\gamma |)}=1/p-1/q}$ , 1<p<(n+|?|)/?${1&lt;p&lt;(n+|\gamma |)/{\alpha }}$ , ?A 1+q/p ' ,? (k,+ n )${\varphi \in A-{1+{q/p^{\prime }},\gamma }(\mathbb {R}-{k,+}^{n})}$ and 1/p+1/p ' =1${{1/p}+{1/p^{\prime }}=1}$ . © 2016 by De Gruyter.en_US
dc.identifier.doi10.1515/gmj-2016-0009
dc.identifier.endpage155
dc.identifier.issn1072-947X
dc.identifier.issue2
dc.identifier.scopus2-s2.0-84973926512en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage143
dc.identifier.urihttps://dx.doi.org/10.1515/gmj-2016-0009
dc.identifier.urihttps://hdl.handle.net/20.500.12403/615
dc.identifier.volume23
dc.identifier.wosWOS:000377453300001en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofGeorgian Mathematical Journalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectB-maximal operator
dc.subjectB-Riesz potential
dc.subjectgeneralized B-Morrey space
dc.subjectB-maximal operator
dc.subjectB-Riesz potential
dc.subjectgeneralized B-Morrey space
dc.titleOn the boundedness of a B-Riesz potential in the generalized weighted B-Morrey spacesen_US
dc.typeArticleen_US

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