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Article

A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function

1
Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
2
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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Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia
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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, 352700 Maykop, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Alina Alb Lupas
Symmetry 2021, 13(2), 351; https://doi.org/10.3390/sym13020351
Received: 28 January 2021 / Revised: 9 February 2021 / Accepted: 17 February 2021 / Published: 21 February 2021
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some special cases as well as some operator expressions are also presented. View Full-Text
Keywords: Hilbert-type integral inequality; weight function; equivalent statement; operator; cosine function Hilbert-type integral inequality; weight function; equivalent statement; operator; cosine function
MDPI and ACS Style

Rassias, M.T.; Yang, B.; Raigorodskii, A. A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function. Symmetry 2021, 13, 351. https://doi.org/10.3390/sym13020351

AMA Style

Rassias MT, Yang B, Raigorodskii A. A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function. Symmetry. 2021; 13(2):351. https://doi.org/10.3390/sym13020351

Chicago/Turabian Style

Rassias, Michael T., Bicheng Yang, and Andrei Raigorodskii. 2021. "A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function" Symmetry 13, no. 2: 351. https://doi.org/10.3390/sym13020351

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