Strong approximation of Fourier series on generalized periodic Morrey spaces

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dc.contributor.author Adilkhanov, A.N.
dc.contributor.author Baituyakova, Zh.Zh.
dc.contributor.author Matin, D.T.
dc.date.accessioned 2019-02-05T06:15:20Z
dc.date.available 2019-02-05T06:15:20Z
dc.date.issued 2018-04
dc.identifier.citation Adilkhanov A.N. Strong approximation of Fourier series on generalized periodic Morrey spaces /A.N.Adilkhanov, Zh.Zh.Baituyakova ,D.T. Matin //Қарағанды универисетінің хабаршысы. МАТЕМАТИКА Сериясы.=Вестник Карагандинского университета. Серия МАТЕМАТИКА.=Bulletin of the Karaganda University. MATHEMATICS Series.-2018.-№2.-Р.8-16 ru_RU
dc.identifier.issn 2518-7929
dc.identifier.uri http://rep.ksu.kz/handle/data/3561
dc.description.abstract In recent years, a lot of attention has been paid to study of Morrey type spaces. Many applications in partial di˙erential equation of Morrey spaces and Lizorkin-Triebel spaces have been given in work G.Di Fazioand, M. Ragusa and the book of T. Mizuhara. The theory of generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, with T. Mizuhara and E. Nakai proposed, are equipped with a parameter and a function. First we give definition of Morrey and generalized Morrey spaces. Then we recall the boundedness of periodic Hilbert transform. This will be our main tool for all wtht follows. In a more or less elementary way, we carry over the known boundedness assertions for the Hilbert transform on Morrey spaces defined on 􀀀 to periodic Morrey spaces. Boundedness of the Hilbert transform implies uniform estimates of the operator norms of the partial sumd of the Fourier series. Then we study vector-valued Fourier-multiplier theorem for smooth multipliers. Afterwards, we study vector valued version of famous Riesz theorem. Here we concentrate on Lizorkin representations. Finally, we get an interesting characterization of the space 􀀀􀀄􀀀􀀁􀀂􀀁􀀃 􀀁􀀀 􀀀 by using di˙erences of partial sums of the Fourier series Finally, we get an interesting characterization of the space 􀀀􀀄􀀀􀀁􀀂􀀁􀀃 􀀁􀀀 􀀀 by using di˙erences of partial sums of the Fourier series and consequence for strong approximation of Fourier series on Morrey space. ru_RU
dc.language.iso en ru_RU
dc.publisher Ye.A.Buketov Karaganda State University Publishing house ru_RU
dc.relation.ispartofseries Bulletin of the Karaganda University. Mathematics series;№ 2(90)/2018
dc.subject Morrey spaces ru_RU
dc.subject generalized periodic Morrey spaces ru_RU
dc.subject strong approximation ru_RU
dc.subject vector-valued version of the Riesz theorem ru_RU
dc.title Strong approximation of Fourier series on generalized periodic Morrey spaces ru_RU
dc.type Article ru_RU


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