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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

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
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1572-9176
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Volume 19, Issue 2

Issues

Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces

Seymur S. Aliev / Vagif S. Guliev
  • Ahi Evran University, Department of Mathematics, Kirsehir, Turkey; and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan
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Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0008

Abstract.

In this paper we study the boundedness of the parametric Marcinkiewicz operator on generalized Morrey spaces . We find the sufficient conditions on the pair which ensure the boundedness of the operators from one generalized Morrey space to another , , and from the space to the weak space . As an application of the above result, the boundedness of the commutator of Marcinkiewicz operators on generalized Morrey spaces is also obtained. In the case , we find the sufficient conditions on the pair which ensure the boundedness of the operators from one generalized Morrey space to another , , and from the space to the weak space . In all the cases the conditions for boundedness are given in terms of Zygmund-type integral inequalities on which do not require any assumption on the monotonicity of .

Keywords: Parametric Marcinkiewicz operator; generalized Morrey space; commutator; BMO

About the article

Received: 2011-04-05

Revised: 2012-02-16

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 195–208, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0008.

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