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Article

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

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Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
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Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia
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Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA
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Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
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Faculty of Bioengineering and Bioinformatics, Moscow State University, 119991 Moscow, Russia
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Institute of Mathematics and Computer Science, Buryat State University, 670000 Ulan-Ude, Russia
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Caucasus Mathematical Center, Adyghe State University, 385012 Maykop, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Ioan Rașa
Symmetry 2021, 13(6), 1006; https://doi.org/10.3390/sym13061006
Received: 13 May 2021 / Revised: 26 May 2021 / Accepted: 1 June 2021 / Published: 4 June 2021
(This article belongs to the Special Issue Various Approaches for Generalized Integral Transforms)
In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering. View Full-Text
Keywords: Hardy-type integral inequality; weight function; equivalent form; operator; norm Hardy-type integral inequality; weight function; equivalent form; operator; norm
MDPI and ACS Style

Rassias, M.T.; Yang, B.; Raigorodskii, A. Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities. Symmetry 2021, 13, 1006. https://doi.org/10.3390/sym13061006

AMA Style

Rassias MT, Yang B, Raigorodskii A. Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities. Symmetry. 2021; 13(6):1006. https://doi.org/10.3390/sym13061006

Chicago/Turabian Style

Rassias, Michael T., Bicheng Yang, and Andrei Raigorodskii. 2021. "Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities" Symmetry 13, no. 6: 1006. https://doi.org/10.3390/sym13061006

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