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dc.contributor.authorGergün, Seçil
dc.contributor.authorKaptanoğlu, H. Turgay
dc.contributor.authorÜreyen, Adem Ersin
dc.date.accessioned2019-10-20T14:28:15Z
dc.date.available2019-10-20T14:28:15Z
dc.date.issued2016
dc.identifier.issn0129-167X
dc.identifier.issn1793-6519
dc.identifier.urihttps://dx.doi.org/10.1142/S0129167X16500701
dc.identifier.urihttps://hdl.handle.net/11421/18071
dc.descriptionWOS: 000384402200002en_US
dc.description.abstractWe initiate a detailed study of two-parameter Besov spaces on the unit ball of R-n consisting of harmonic functions whose sufficiently high-order radial derivatives lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels are weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. Estimates of the growth of kernels lead to characterization of integral transformations on Lebesgue classes. The transformations allow us to conclude that the order of the radial derivative is not a characteristic of a Besov space as long as it is above a certain threshold. Using kernels, we define generalized Bergman projections and characterize those that are bounded from Lebesgue classes onto Besov spaces. The projections provide integral representations for the functions in these spaces and also lead to characterizations of the functions in the spaces using partial derivatives. Several other applications follow from the integral representations such as atomic decomposition, growth at the boundary and of Fourier coefficients, inclusions among them, duality and interpolation relations, and a solution to the Gleason problem.en_US
dc.description.sponsorshipTUBITAK [108T329]en_US
dc.description.sponsorshipThis research is partially supported by TUBITAK under Research Project Grant 108T329.en_US
dc.language.isoengen_US
dc.publisherWorld Scientific Publ Co Pte LTDen_US
dc.relation.isversionof10.1142/S0129167X16500701en_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectSpherical Harmonicen_US
dc.subjectZonal Harmonicen_US
dc.subjectGegenbauer (Ultraspherical) Polynomialen_US
dc.subjectPoisson Kernelen_US
dc.subjectReproducing Kernelen_US
dc.subjectRadial Fractional Derivativeen_US
dc.subjectMobius Transformationen_US
dc.subjectBergman Spaceen_US
dc.subjectBesov Spaceen_US
dc.subjectHardy Spaceen_US
dc.subjectBergman Projectionen_US
dc.subjectAtomic Decompositionen_US
dc.subjectBoundary Growthen_US
dc.subjectFourier Coefficienten_US
dc.subjectDualityen_US
dc.subjectInterpolationen_US
dc.subjectGleason Problemen_US
dc.titleHarmonic Besov spaces on the ballen_US
dc.typearticleen_US
dc.relation.journalInternational Journal of Mathematicsen_US
dc.contributor.departmentAnadolu Üniversitesi, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume27en_US
dc.identifier.issue9en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US]
dc.contributor.institutionauthorÜreyen, Adem Ersin


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