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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


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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
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/ 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 Iα in the local Morrey–Lorentz spaces Mp,q;λloc(n). 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 Mp,q;λloc(n).

Keywords: Local Morrey–Lorentz space; Riesz potential; Hardy operator

MSC 2010: 42B20; 42B35; 47G10

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About the article

Received: 2016-06-17

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, DOI: https://doi.org/10.1515/gmj-2018-0065.

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