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This article is cited in 6 scientific papers (total in 6 papers)
Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces
A. Akbuluta, I. Ekincioglub, A. Serbetcic, T. Tararykovad a Ahi Evran University, Department of Mathematics, Kirşehir, Turkey
b Department of Mathematics, Dumlupinar University, Kütahya, Turkey
c Ankara University, Department of Mathematics, Tandogan-Ankara, Turkey
d Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Abstract:
In this paper we study the boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces. We reduce this problem to the problem of boundedness of the supremal operator in weighted $L_p$-spaces on the cone of non-negative non-decreasing functions. This makes it possible to derive sharp sufficient conditions for boundedness for all admissible values of the numerical parameters, which, for a certain range of the numerical parameters, coincide with the necessary ones.
Keywords and phrases:
anisotropic fractional maximal operator, anisotropic local and global Morrey-type spaces, supremal operator on the cone of monotonic functions.
Received: 05.03.2011
Citation:
A. Akbulut, I. Ekincioglu, A. Serbetci, T. Tararykova, “Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces”, Eurasian Math. J., 2:2 (2011), 5–30
Linking options:
https://www.mathnet.ru/eng/emj50 https://www.mathnet.ru/eng/emj/v2/i2/p5
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