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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
ISSN
1572-9176
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Volume 6, Issue 1

Issues

Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups

V. Kokilashvili
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ A. Meskhi
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-02-24 | DOI: https://doi.org/10.1515/GMJ.1999.65

Abstract

The optimal sufficient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces defined on homogeneous groups. In some particular case the found conditions are necessary for the corresponding inequalities to be valid. Also, the necessary and sufficient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces defined on homogeneous groups.

Key words and phrases.: Hilbert transform; singular integrals; Hardy operator; Lorentz spaces; two-weighted inequality; homogeneous groups

About the article

Received: 1996-11-21

Published Online: 2010-02-24

Published in Print: 1999-02-01


Citation Information: Georgian Mathematical Journal, Volume 6, Issue 1, Pages 65–82, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.1999.65.

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