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# Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

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1572-9176
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# Riesz potential in the local Morrey–Lorentz spaces and some applications

Vagif S. Guliyev
• Institute of Mathematics and Mechanics, Baku, Azerbaijan; and Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
• Email
• Other articles by this author:
/ Abdulhamit Kucukaslan
/ Canay Aykol
/ Ayhan Serbetci
Published Online: 2018-10-30 | DOI: https://doi.org/10.1515/gmj-2018-0065

## Abstract

In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential ${I}_{\alpha }$ in the local Morrey–Lorentz spaces ${M}_{p,q;\lambda }^{\mathrm{loc}}\left({ℝ}^{n}\right)$. This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces ${M}_{p,q;\lambda }^{\mathrm{loc}}\left({ℝ}^{n}\right)$.

MSC 2010: 42B20; 42B35; 47G10

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Revised: 2016-10-10

Accepted: 2017-01-12

Published Online: 2018-10-30

The research of V. S. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1.

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X,

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