Geodesic
Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces
Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 5-30.

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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. 
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A. Akbulut; I. Ekincioglu; A. Serbetci; T. Tararykova. Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces. Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 5-30. http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a0/

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