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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Autores principales:	He Bing, Hong Yong, Chen Qiang
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/88798f86fd4e4038bbd7f65d459cdb24
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spelling	oai:doaj.org-article:88798f86fd4e4038bbd7f65d459cdb242021-12-05T14:10:52ZThe equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications2391-545510.1515/math-2021-0023https://doaj.org/article/88798f86fd4e4038bbd7f65d459cdb242021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0023https://doaj.org/toc/2391-5455In 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.He BingHong YongChen QiangDe Gruyterarticlemultiple integral half-discrete hilbert-type inequalitynonhomogeneous kernelequivalent parameter conditionbest constant factoroperator normbounded operator26d1547a07MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 400-411 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07 Mathematics QA1-939
spellingShingle	multiple integral half-discrete hilbert-type inequality nonhomogeneous kernel equivalent parameter condition best constant factor operator norm bounded operator 26d15 47a07 Mathematics QA1-939 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
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.
format	article
author	He Bing Hong Yong Chen Qiang
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
publishDate	2021
url	https://doaj.org/article/88798f86fd4e4038bbd7f65d459cdb24
work_keys_str_mv	AT hebing theequivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications AT hongyong theequivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications AT chenqiang theequivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications AT hebing equivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications AT hongyong equivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications AT chenqiang equivalentparameterconditionsforconstructingmultipleintegralhalfdiscretehilberttypeinequalitieswithaclassofnonhomogeneouskernelsandtheirapplications
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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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