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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

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1572-9176
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Volume 19, Issue 2

Issues

On grand Lorentz spaces and the maximal operator

Pankaj Jain / Santosh Kumari
Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0010

Abstract.

The notion of the classical Lorentz space is generalized to the grand Lorentz space . Some basic properties of the space are proved and the boundedness of the maximal operator M is characterized in . It is shown that is bounded if and only if the weight w belongs to the famous -class.

Keywords: Lorentz space; grand Lorentz space; grand Lebesgue space; maximal operator; averaging operator; -class; -class

About the article

Received: 2011-07-01

Revised: 2012-01-31

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 235–246, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0010.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

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[1]
Pankaj Jain, Monika Singh, and Arun Pal Singh
Indagationes Mathematicae, 2017, Volume 28, Number 2, Page 516
[2]
Pankaj Jain, Monika Singh, and Arun Pal Singh
Transactions of A. Razmadze Mathematical Institute, 2016, Volume 170, Number 1, Page 34

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