Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p...

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Main Authors: Qiang Chen, Bing He, Yong Hong, Zhen Li
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/7414861
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spelling doaj-f47c67553b3e4a3391a28d5a2c9b3da32020-11-25T03:35:24ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/74148617414861Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous KernelQiang Chen0Bing He1Yong Hong2Zhen Li3Department of Computer Science, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Guangdong Baiyun University, Guangzhou 510450, ChinaCollege of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, ChinaLet Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed.http://dx.doi.org/10.1155/2020/7414861
collection DOAJ
language English
format Article
sources DOAJ
author Qiang Chen
Bing He
Yong Hong
Zhen Li
spellingShingle Qiang Chen
Bing He
Yong Hong
Zhen Li
Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
Journal of Function Spaces
author_facet Qiang Chen
Bing He
Yong Hong
Zhen Li
author_sort Qiang Chen
title Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
title_short Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
title_full Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
title_fullStr Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
title_full_unstemmed Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
title_sort equivalent parameter conditions for the validity of half-discrete hilbert-type multiple integral inequality with generalized homogeneous kernel
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed.
url http://dx.doi.org/10.1155/2020/7414861
work_keys_str_mv AT qiangchen equivalentparameterconditionsforthevalidityofhalfdiscretehilberttypemultipleintegralinequalitywithgeneralizedhomogeneouskernel
AT binghe equivalentparameterconditionsforthevalidityofhalfdiscretehilberttypemultipleintegralinequalitywithgeneralizedhomogeneouskernel
AT yonghong equivalentparameterconditionsforthevalidityofhalfdiscretehilberttypemultipleintegralinequalitywithgeneralizedhomogeneouskernel
AT zhenli equivalentparameterconditionsforthevalidityofhalfdiscretehilberttypemultipleintegralinequalitywithgeneralizedhomogeneouskernel
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