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

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

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 e...

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Main Authors: Michael Th. Rassias, Bicheng Yang, Andrei Raigorodskii
Format: Article
Language:English
Published: MDPI AG 2021-02-01
Series:Symmetry
Subjects:
Hilbert-type integral inequality
weight function
equivalent statement
operator
cosine function
Online Access:https://www.mdpi.com/2073-8994/13/2/351
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spelling doaj-abd1931f63ff436497035277b872c9ed2021-02-22T00:04:04ZengMDPI AGSymmetry2073-89942021-02-011335135110.3390/sym13020351A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent FunctionMichael Th. Rassias0Bicheng Yang1Andrei Raigorodskii2Institute of Mathematics, University of Zurich, CH-8057 Zurich, SwitzerlandDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaMoscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, RussiaIn 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.https://www.mdpi.com/2073-8994/13/2/351Hilbert-type integral inequalityweight functionequivalent statementoperatorcosine function
collection DOAJ
language English
format Article
sources DOAJ
author Michael Th. Rassias
Bicheng Yang
Andrei Raigorodskii
spellingShingle Michael Th. Rassias
Bicheng Yang
Andrei Raigorodskii
A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
Symmetry
Hilbert-type integral inequality
weight function
equivalent statement
operator
cosine function
author_facet Michael Th. Rassias
Bicheng Yang
Andrei Raigorodskii
author_sort Michael Th. Rassias
title A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
title_short A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
title_full A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
title_fullStr A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
title_full_unstemmed A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
title_sort hilbert-type integral inequality in the whole plane related to the arc tangent function
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-02-01
description 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.
topic Hilbert-type integral inequality
weight function
equivalent statement
operator
cosine function
url https://www.mdpi.com/2073-8994/13/2/351
work_keys_str_mv AT michaelthrassias ahilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
AT bichengyang ahilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
AT andreiraigorodskii ahilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
AT michaelthrassias hilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
AT bichengyang hilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
AT andreiraigorodskii hilberttypeintegralinequalityinthewholeplanerelatedtothearctangentfunction
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