A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms

A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms

We establish a new inequality of Hilbert-type containing positive homogeneous kernel <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <mi>min</mi> <mo>{</mo&g...

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Bibliographic Details
Main Authors: Bicheng Yang, Shanhe Wu, Aizhen Wang
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Symmetry
Subjects:
hilbert-type inequality
homogeneous kernel
equivalent statement
operator expression
euler–maclaurin summation formula
Online Access:https://www.mdpi.com/2073-8994/12/3/342
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spelling doaj-a1a7be95b1994380b8db5ddf05801b4d2020-11-24T21:54:07ZengMDPI AGSymmetry2073-89942020-02-0112334210.3390/sym12030342sym12030342A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent FormsBicheng Yang0Shanhe Wu1Aizhen Wang2Institute of Applied Mathematics, Longyan University, Longyan 364012, Fujian, ChinaDepartment of Mathematics, Longyan University, Longyan 364012, Fujian, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, Guangdong, ChinaWe establish a new inequality of Hilbert-type containing positive homogeneous kernel <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <mi>min</mi> <mo>{</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>}</mo> <mo stretchy="false">)</mo> </mrow> <mi>&#955;</mi> </msup> </mrow> </semantics> </math> </inline-formula> and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.https://www.mdpi.com/2073-8994/12/3/342hilbert-type inequalityhomogeneous kernelequivalent statementoperator expressioneuler–maclaurin summation formula
collection DOAJ
language English
format Article
sources DOAJ
author Bicheng Yang
Shanhe Wu
Aizhen Wang
spellingShingle Bicheng Yang
Shanhe Wu
Aizhen Wang
A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
Symmetry
hilbert-type inequality
homogeneous kernel
equivalent statement
operator expression
euler–maclaurin summation formula
author_facet Bicheng Yang
Shanhe Wu
Aizhen Wang
author_sort Bicheng Yang
title A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
title_short A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
title_full A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
title_fullStr A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
title_full_unstemmed A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
title_sort new hilbert-type inequality with positive homogeneous kernel and its equivalent forms
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-02-01
description We establish a new inequality of Hilbert-type containing positive homogeneous kernel <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <mi>min</mi> <mo>{</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>}</mo> <mo stretchy="false">)</mo> </mrow> <mi>&#955;</mi> </msup> </mrow> </semantics> </math> </inline-formula> and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.
topic hilbert-type inequality
homogeneous kernel
equivalent statement
operator expression
euler–maclaurin summation formula
url https://www.mdpi.com/2073-8994/12/3/342
work_keys_str_mv AT bichengyang anewhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
AT shanhewu anewhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
AT aizhenwang anewhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
AT bichengyang newhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
AT shanhewu newhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
AT aizhenwang newhilberttypeinequalitywithpositivehomogeneouskernelanditsequivalentforms
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