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 Eurasian Math. J., 2011, Volume 2, Number 2, Pages 5–30 (Mi emj50)

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.

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MSC: 42B20, 42B25, 42B35
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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

Citation in format AMSBIB
\Bibitem{AkbEkiSer11} \by A.~Akbulut, I.~Ekincioglu, A.~Serbetci, T.~Tararykova \paper Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces \jour Eurasian Math. J. \yr 2011 \vol 2 \issue 2 \pages 5--30 \mathnet{http://mi.mathnet.ru/emj50} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2910829} \zmath{https://zbmath.org/?q=an:1254.42019} 

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This publication is cited in the following articles:
1. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32
2. V. S. Guliyev, “Generalized weighted Morrey spaces and higher order commutators of sublinear operators”, Eurasian Math. J., 3:3 (2012), 33–61
3. A. Akbulut, V. S. Guliev, Sh. A. Muradova, “On the boundedness of the anisotropic fractional maximal operator from anisotropic complementary Morrey-type spaces to anisotropic Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 7–20
4. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45
5. Guliyev V.S., Hasanov S.G., Sawano Y., “Decompositions of Local Morrey-Type Spaces”, Positivity, 21:3 (2017), 1223–1252
6. Ruzhansky M., Suragan D., Yessirkegenov N., “Hardy-Littlewood, Bessel-Riesz, and Fractional Integral Operators in Anisotropic Morrey and Campanato Spaces”, Fract. Calc. Appl. Anal., 21:3 (2018), 577–612
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