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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 18, Issue 3

Issues

A note on Lorentz–Zygmund spaces

Hiroto Oba
  • Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, 990-8560, Japan.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Enji Sato / Yuichi Sato
  • Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, 990-8560, Japan.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/gmj.2011.0035

Abstract

Let 1 ≤ q < p < ∞, and ℝ be the real line. Hörmander showed that any bounded linear translation invariant operator from Lp (ℝ) to Lq (ℝ) is trivial. Blozinski obtained an analogy to Hörmander in Lorentz spaces on the real line. In this paper, we generalize Blozinski's result in Lorentz–Zygmund spaces. Also, Bochkarev proved an inequality related to the Hausdorff–Young–Riesz theorem in Lorentz spaces, and the sharpness of the inequality. We improve Bochkarev's inequality in Lorentz–Zygmund spaces, and prove the sharpness of our inequality.

Keywords.: Hausdorff–Young theorem; Lorentz–Zygmund space

About the article

Received: 2009-01-22

Published Online: 2011-07-14

Published in Print: 2011-09-01


Citation Information: Georgian Mathematical Journal, Volume 18, Issue 3, Pages 533–548, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2011.0035.

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