Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

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dc.contributor.authorGuliyev, Emin
dc.contributor.authorEroglu, Ahmet
dc.contributor.authorMammadov, Yagub
dc.date.accessioned2019-08-01T13:38:39Z
dc.date.available2019-08-01T13:38:39Z
dc.date.issued2010
dc.departmentNiğde ÖHÜ
dc.description.abstractWe consider the generalized shift operator, associated with the Dunkl operator Lambda(alpha)(f)(x) = (d/dx)f(x) + ((2 alpha + 1)/x)((f(x) - f(-x))/2), alpha > -1/2. We study the boundedness of the Dunkltype fractional maximal operator M(beta) in the Dunkl-type Morrey space L(p,lambda,alpha)(R), 0 <= lambda < 2 alpha + 2. We obtain necessary and sufficient conditions on the parameters for the boundedness M(beta), 0 <= beta < 2 alpha + 2 from the spaces L(p,lambda,alpha)(R) to the spaces L(q,lambda,alpha)(R), 1 < p <= q < infinity, and from the spaces L(1,lambda,alpha)(R) to the weak spaces WL(q,lambda,alpha)(R), 1 < q < infinity. As an application of this result, we get the boundedness of M beta from the Dunkl-type Besov-Morrey spaces Bp theta,lambda,alpha s(R) to the spaces Bq theta,lambda,alpha s(R), 1 < p <= q < infinity, 0 <= lambda < 2 alpha + 2, 1/p - 1/q = beta/(2 alpha + 2 - lambda), 1 <= theta <= infinity, and 0 < s < 1.
dc.identifier.doi10.1155/2010/976493
dc.identifier.issn1085-3375
dc.identifier.scopus2-s2.0-77955387211
dc.identifier.scopusqualityQ4
dc.identifier.urihttps://dx.doi.org/10.1155/2010/976493
dc.identifier.urihttps://hdl.handle.net/11480/4930
dc.identifier.wosWOS:000280762600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthor[0-Belirlenecek]
dc.language.isoen
dc.publisherHINDAWI PUBLISHING CORPORATION
dc.relation.ispartofABSTRACT AND APPLIED ANALYSIS
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleNecessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces
dc.typeArticle

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