The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications

In this paper, we establish equivalent parameter conditions for the validity of multiple integral half-discrete Hilbert-type inequalities with the nonhomogeneous kernel G(nλ1∥x∥m,ρλ2)G\left({n}^{{\lambda }_{1}}\parallel x{\parallel }_{m,\rho }^{{\lambda }_{2}}\hspace{-0.16em}) (λ1λ2>0{\lambda }_{...

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Main Authors:	He Bing, Hong Yong, Chen Qiang
Format:	Article
Language:	English
Published:	De Gruyter 2021-05-01
Series:	Open Mathematics
Subjects:	multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07
Online Access:	https://doi.org/10.1515/math-2021-0023

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spelling	doaj-88798f86fd4e4038bbd7f65d459cdb242021-10-03T07:42:35ZengDe GruyterOpen Mathematics2391-54552021-05-0119140041110.1515/math-2021-0023The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applicationsHe Bing0Hong Yong1Chen Qiang2Department of Mathematics, Guangdong University of Education, Guangzhou, ChinaDepartment of Applied Mathematics, Guangzhou Huashang College, Guangzhou, ChinaDepartment of Computer Science, Guangdong University of Education, Guangzhou, ChinaIn this paper, we establish equivalent parameter conditions for the validity of multiple integral half-discrete Hilbert-type inequalities with the nonhomogeneous kernel G(nλ1∥x∥m,ρλ2)G\left({n}^{{\lambda }_{1}}\parallel x{\parallel }_{m,\rho }^{{\lambda }_{2}}\hspace{-0.16em}) (λ1λ2>0{\lambda }_{1}{\lambda }_{2}\gt 0) and obtain best constant factors of the inequalities in specific cases. In addition, we also discuss their applications in operator theory.https://doi.org/10.1515/math-2021-0023multiple integral half-discrete hilbert-type inequalitynonhomogeneous kernelequivalent parameter conditionbest constant factoroperator normbounded operator26d1547a07
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	He Bing Hong Yong Chen Qiang
spellingShingle	He Bing Hong Yong Chen Qiang The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications Open Mathematics multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07
author_facet	He Bing Hong Yong Chen Qiang
author_sort	He Bing
title	The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
title_short	The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
title_full	The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
title_fullStr	The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
title_full_unstemmed	The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
title_sort	equivalent parameter conditions for constructing multiple integral half-discrete hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
publisher	De Gruyter
series	Open Mathematics
issn	2391-5455
publishDate	2021-05-01
description	In this paper, we establish equivalent parameter conditions for the validity of multiple integral half-discrete Hilbert-type inequalities with the nonhomogeneous kernel G(nλ1∥x∥m,ρλ2)G\left({n}^{{\lambda }_{1}}\parallel x{\parallel }_{m,\rho }^{{\lambda }_{2}}\hspace{-0.16em}) (λ1λ2>0{\lambda }_{1}{\lambda }_{2}\gt 0) and obtain best constant factors of the inequalities in specific cases. In addition, we also discuss their applications in operator theory.
topic	multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07
url	https://doi.org/10.1515/math-2021-0023
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The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications

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