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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

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Volume 26, Issue 1

Issues

On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces

Alexander Meskhi
  • Department of Mathematical Analysis, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili Str., Tbilisi 0177; and Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77 Kostava St., Tbilisi, 0175, Georgia
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  • Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan; and Departamento de Matemáticas, Facultad de Ciencias, Pontificia Universidad Javeriana, Bogota, Colombia
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Published Online: 2017-11-29 | DOI: https://doi.org/10.1515/gmj-2017-0050

Abstract

In this paper, we obtain the boundedness of the Marcinkiewicz integral on continual Herz spaces with variable exponent, where all parameters defining the space are variable.

Keywords: Herz spaces; variable exponent spaces; Marcinkiewicz integral

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About the article

Received: 2016-02-12

Accepted: 2017-02-28

Published Online: 2017-11-29

Published in Print: 2019-03-01


The second-named author was partially supported by the research project “Study of boundedness of operators in generalized Morrey spaces”, ID-PRJ: 6576, of the Faculty of Sciences of Pontificia Universidad Javeriana, Bogotá, Colombia. The third-named author was supported by Pontificia Universidad Javeriana, Bogotá, Colombia, as a Post-Doctoral investigator working on the research project “Study of boundedness of some operators in generalized Morrey spaces”, ID-PRJ: 6576 (Contract Number: DPE-040-15).


Citation Information: Georgian Mathematical Journal, Volume 26, Issue 1, Pages 105–116, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0050.

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